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PUBLICATIONS

This is the list of publications and preprints beginning in 2003.

Published Books & Special Journal Issues

  
  • G. Cortiñas, E. Friedlander, C. Haesemeyer, Eds. Special issue dedicated to Chuck Weibel on the occasion of his 65th birthday. Journal of Pure and Applied Algebra, Volume 221, Issue 7 pp. 1495-1898 (July 2017).

  • G. Cortiñas, Ed.  Topics in Noncommutative Geometry. Clay Mathematics Institute Proceedings, Vol 16.
  • P. F. Baum, G. Cortiñas, R. Meyer, R. Sánchez-García, M. Schlichting, B. Toën. Topics in algebraic and topological K-theory. Springer Lecture Notes in Mathematics 2008. Publisher's website  pdf
  • G. Cortiñas, J. Cuntz, M. Karoubi, R. Nest. K-Theory and Noncommutative Geometry: Connections and Applications to Other Areas of Mathematics. European Mathematical Society Publishing House, 2008. Publisher's website

Published Papers (since 2003)

   

      2024


  •  G Cortiñas, D. Mukherjee. A Quillen model structure of local homotopy equivalences. Theory and Applications of Categories 41 (2024) 268-287. doi

      2023


  •    G. Arnone, Lifting morphisms between graded Grothendieck groups of Leavitt path algebras. Journal of Algebra 631 (2022) 804-829 doi, arXiv
  •    G. Cortiñas. Classifying Leavitt path algebras up to involution preserving homotopy. Math. Annalen 386pages 2107–2157 (2023). doi

2022


  • G. Arnone, G Cortiñas. Graded $K$-theory and Leavitt path algebras. J. of Algebraic Combinatorics. doi arXiv
  • G. Cortiñas. Classifying Leavitt path algebras up to involution preserving homotopy. Mathematische Annalen. doi  arXiv
  • G Cortiñas. Lifting graph C*-algebra maps to Leavitt path algebra maps. Bulletin of the London Mathematical Society, 2022. doi arXiv
  • G. Cortiñas, S. Vega. Bivariant Hermitian $K$-theory and Karoubi's fundamental theorem. Journal of Pure and Applied Algebra 226:12 107124 arXiv doi
  • G. Arnone, G. Cortiñas. Nonexistence of graded unital homomorphisms between Leavitt algebras and their Cuntz splices. Journal of Algebra and its Applications. doi. arXiv

2021

  • G. Cortiñas, D. Montero. Algebraic bivariant K-theory and Leavitt path algebras.Journal of Noncommutative Geometry, 15 (2021) 113-146. doi, arXiv
  • E. Jespers, L. Kubat, A. Van Antwerpen, L. Vendramin. Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation, Adv. Math. 385 (2021), 107767
  • A. Konovalov, A. Smoktunowicz, L. Vendramin. On skew braces and their ideals. Exp. Math. 30 (2021), no. 1, 95–104
  • Jorge A. Guccione,  Juan J. Guccione. Comparison of two notions of weak crossed products. Journal of Algebra and Its Applications 20 (4) 2150059 (2021).

2020


  • E. Acri, R. Lutowski, L. Vendramin. Retractability of solutions to the Yang-Baxter equation and p- nilpotency of skew braces. Internat. J. Algebra Comput. 30 (2020), no. 1, 91–115 7
  • G. Cortiñas, R. Meyer, D. Mukherjee. Nonarchimedean analytic cyclic homology. Documenta Mathematica 25, 1353--1419. doi
  • A. Smoktunowicz, L. Vendramin, R. Weston. Combinatorial solutions to the re f lection equation. J. Algebra 549 (2020) 268–290 8
  • M. Farinati, Hopfological algebra for infinite dimensional Hopf algebras. Algebras and Representation Theory (2020), doi arXiv
  • M. Farinati, G.A. García Quantum function algebras from finite-dimensional Nichols algebras. Journal of Non Commutative Geometry vol 14(3), (2020), 879-911., DOI: 10.4171/JNCG/381 arXiv
  • G. Cortiñas, D. Montero, Homotopy classification of Leavitt path algebras. Advances in Mathematics 362 (2020), doiarXiv
  • G. Cortiñas, R. Meyer, D. Mukherjee. Nonarchimedean analytic cyclic homology. Documenta Mathematica 25 (2020), 1353--1419. doi
  • Jorge A. Guccione, Juan J. Guccione , Christian Valqui. Cleft extensions of weak Hopf algebras. Journal of Algebra 547 (2020) 668-710.

2019


  • M. Farinati, J. Garcia Galofre. Virtual link and knot invariants from non-abelian Yang-Baxter 2-cocycle pairs. Osaka Journal of Mathematics 56(3) (2019) 525-547. arXiv
  • E. Jespers, L. Kubat, A. Van Antwerpen, L. Vendramin. Factorization of skew braces. Math. Ann. 375 (2019), no. 3-4, 1649–1663 6
  • E. Rodríguez Cirone. The homotopy groups of the simplicial mapping space between algebras. Documenta Mathematica, 24 (2019), 251-270.
  •  G. Cortiñas, M.E. Rodríguez, L^p-operator algebras associated with oriented graphs. Journal of Operator Theory 81 (2019), 225-254. doi
  • F. Cedó, A. Smoktunowicz, L. Vendramin. Skew left braces of nilpotent type. Proc. Lond. Math. Soc. (3) 118 (2019), no. 6, 1367-1392.
  • L. Vendramin. Problem on skew braces. Adv. Group Theory Appl. 7 (2019), 15-37
  • V. Lebed, L. Vendramin. On structure groups of set-theoretic solution to the Yang-Baxter equation. Proc. Edinb. Math. Soc. (2) 62 (2019), no. 3, 683-717
  • I. Heckenbeger, L. Vendramin. PBW deformations of a Fomin-Kirillov algebra and other examples. Algebr. Represent. Theory 22 (2019), no. 6, 1513–1532
  •  Jorge A. Guccione, Juan J. Guccione, C. Valqui. Solutions of the braid equation and orders. Algebras and Representation Theory 22(3) (2019) 665-697.

2018

  • J. Arce, J. A. Guccione, J. J. Guccione, C. Valqui, Twisted tensor products of Kn with Km , Algebras and Representation Theory 22(6) (2018) 15991651.
  • J. Beltran - M. Farinati - E. G. Reyes. Central extensions of the algebra of formal pseudo-differential symbols via Hochschild (co)homology and quadratic symplectic Lie algebras, Journal of Pure and Applied Algebra Volume 222, Issue 8, August 2018, Pages 2006-2021
  • M. Farinati - P. Jancsa. Lie bialgebra structures on 2-step nilpotent graph algebras, Journal of Algebra Volume 505, 1 July 2018, Pages 70-91. ArXiv:math/1602220
  • G. Cortiñas, G. Tartaglia. Compact operators and algebraic K-theory for groups which act properly and isometrically on Hilbert space. J. reine angew. Math. 734 (2018), 265-292.

  • G. Cortiñas, C. Haesemeyer, M.E. Walker, C. Weibel. The K-theory of toric schemes over regular rings of mixed characteristic.
    Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Festschrift for Antonio Campillo on the Occasion
    of his 65th Birthday. Gert-Martin Greuel, Luis Narváez and Sebastá Xambó-Descamps, Eds. Springer, 2018. Pages 455-479.
    doi
  • G. Cortiñas, J. Cuntz, R. Meyer, G. Tamme. Weak completions, bornologies and rigid cohomology. Journal of Geometry and Physics 129, 192-199 (2018). doi
  • G. Cortiñas, J. Cuntz, R. Meyer, G. Tamme. Nonarchimedean bornologies and rigid cohomology. Documenta Mathematica 23, 1197-1245 (2018). doi
  • D. Bachiller, F. Cedó, L. Vendramin. A characterization of finite multipermutation solutions of the Yang-Baxter equation. Publ. Mat. 62 (2018), no. 2, 641-649
  • A. Smoktunowicz, L. Vendramin. On skew braces (with an appendix by N. Byott). J. Comb. Algebra 2 (2018), no. 1, 47–86
  • J. A. Guccione, J. J. Guccione, L. Vendramin. Yang-Baxter operators in symmetric categories. Comm. Algebra 46 (2018), no. 7, 2811--2845
  •  Jorge A. Guccione, Juan J. Guccione, Christian Valqui. Cyclic homology of cleft extensions of algebras. Journal of Algebra and its Applications 17(5), 1850091 (2018)
  • 2017


    • I. Angiono, C. Galindo, L. Vendramin. Hopf braces and Yang-Baxter operators. Proc. Amer. Math. Soc. 145 (2017), no. 5, 1981-1995
    • I. Heckenberger, L. Vendramin. A classification of Nichols algebras of semi-simple Yetter-Drinfeld modules over non-abelian groups. J. Eur. Math. Soc. (JEMS) 19 (2017), no. 2, 299-356
    • I. Heckenberger, L. Vendramin. The classification of Nichols algebras over groups with finite root system of rank two. J. Eur. Math. Soc. (JEMS) 19 (2017), no. 7, 1977-2017
    • V. Lebed, L. Vendramin. Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation. Adv. Math. 304 (2017), 1219-1261
    • L. Guarnieri, L. Vendramin. Skew braces and the Yang-Baxter equation. Math. Comp. 86 (2017), no. 307, 2519-2534
    • L. Vendramin. Doubly transitive groups and cyclic quandles. J. Math. Soc. Japan 69 (2017), no. 3, 1051-1057
    • A. García Iglesias, L. Vendramin. An explicit description of the second cohomology group of a quandle. Math. Z. 286 (2017), no. 3-4, 1041-1063
    • Jorge A. Guccione, Juan J. Guccione, Mauricio da Rocha. Cleft extensions of a family of braided Hopf algebras. Communications in Algebra 45 (2017) 3166-3205.
    • Christian Valqui, Jorge A. Guccione, Juan J. Guccione. On the shape of possible counterexamples to the Jacobian Conjecture. Journal of Algebra 71 (2017) 1374.

2016


  • M. Farinati - J. Garcia Galofre. A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation, Journal of Pure and Applied Algebra Volume 220, Issue 10, 2016, Pages 3454-3475. ArXiv:math/1508.07970.
  • M. Farinati - J. Garcia Galofre. Link and knot invariants from non-abelian Yang-Baxter 2-cocycles, Journal of Knot Theory and its Ramifications, 2016, Vol 25 Nro. 13. ArXiv:math/1507.02232.
  • G. Cortiñas, E. Rodríguez Cirone. Singular coefficients in the K-theoretic Farrell-Jones conjecture. Algebr. Geom. Topol. 16 (2016) 129-147. doi
  • V. Lebed, L. Vendramin. Cohomology and extensions of braces.  Pacific J. Math. 284 (2016), no. 1, 191-212 . arXiv
  • L. Vendramin. Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova. J. Pure Appl. Alg. 220 (2016), no. 5, 1681-2076. arXiv
  • W. E. Clark, M. Saito, L. Vendramin. Quandle coloring and cocycle invariants of composite knots and abelian extensions, J. Knot Theory Ramifications 25 (2016), no. 5, 1650024, 34 pp.  arXiv

2015


  • M. Farinati - L. Lombardi. A Cacti theoretical interpretation of the axioms of bialgebras and H-module algebras, Journal of Algebra 427,1 (2015), pp. 295-316. ArXiv:math/1404.5225.
  • M. Farinati - A.P. Jancsa. Three dimensional real Lie bialgebras Revista de la U.M.A. Vol 56,1, (2015). ArXiv:math/1007.3796.
  • B. Abadie, G. Cortiñas. Homotopy invariance through small stabilizations. J. Homotopy Relat. Struct. September 2015, Volume 10, Issue 3, pp 459-493 doi.
  • G. Cortiñas, C. Haesemeyer, M.E. Walker, C. Weibel. Toric varieties, monoid schemes and cdh descent. J. reine angew. Math. 698, 1-54 (2015).doi
  • J. Dong, S. Natale, L. Vendramin. Frobenius property for fusion categories of small integral dimension, J. Algebra Appl. 14 (2015), no. 2, 1550011 (17 pages). arXiv
  • I. Heckenberger, L. Vendramin. Nichols algebras over groups with finite root systems of rank two III, J. Algebra 422 (2015), 223–256. arXiv
  • I. Heckenberger, A. Lochmann, L. Vendramin. Nichols algebras with many cubic relations. Trans. Amer. Math. Soc. 367 (2015), no. 9, 6315-6356 . arXiv

2014


  • G. Cortiñas. Excision, descent, and singularity in algebraic K-theory. Procedings of ICM, 2014, Seoul, 143--162. arXiv
  • G. Cortiñas, Cyclic homology, tight crossed products, and small stablizations. J. Noncommut. Geom.,  8(4) 1191-1223 (2014).
  • G. Cortiñas, E. Ellis. Isomorphism conjectures with proper coefficients. J. Pure Appl. Algebra 218 (2014),no. 7, 1224-1263.
  • G. Cortiñas, C. Haesemeyer, M.E. Walker, C. Weibel. The K-theory of toric varieties in positive characteristic.
    J. Topol., (2014) 7 (1):247-286.
  • G. Cortiñas, G. Tartaglia. Trace class operators, regulators, and assembly maps in K-theory. Doc. Math., 19 (2014) 439--455.
  • G. Cortiñas, G. Tartaglia. Operator ideals and assembly maps in K-theory. Proc. Amer. Math. 142 (2014), 1089-1099.
  • M. Farinati, J. A. Guccione, J. J. Guccione, The homology of free racks and quandles, Communications in Algebra, 42 (8) (2014) 3593-3506.
  • J. A. Guccione, J. J. Guccione, C. Valqui, The Dixmier conjecture and the shape of possible counterexamples, Journal of Algebra 399 (2014) 581-633.
  • E. Ellis, Equivariant algebraic kk-theory and adjointness theorems. J. Algebra, Volume 398, 15 January 2014, Pages 200–226. arXiv
  • I. Heckenberger, L. Vendramin. Nichols algebras over groups with finite root systems of rank two II, J. Group Theory 17 (2014), no. 6, 1009--1034. arXiv
  • 2013


    • M. Farinati - A.P. Jancsa. Trivial central extensions of Lie bialgebras, Journal of Algebra 390 (2013) 56-76 ArXiv:math/1110.1072.
    • B. Abadie, G. Cortiñas. Homotopy invariance through small stabilizations. J. Homotopy Relat. Struct., doi
    • P. Ara, G. Cortiñas. Tensor products of Leavitt path algebras.   Proc. Amer. Math. Soc., 141(8) 2629–2639. arXiv
    • G. Cortiñas, C. Haesemeyer, M. E. Walker, C. Weibel. K-theory of cones of smooth varieties.  Journal of Algebraic Geometry 22 (2013) 13-34. arXiv
    • F. Fantino, L. Vendramin, On twisted conjugacy classes of type D in sporadic simple groups, Hopf Algebras and Tensor Categories, Contemp. Math. 585 (2013) 247-259. arXiv
    • L. Vendramin. Fomin-Kirillov algebras, Nichols algebras and Weyl groupoids, Oberwolfach Rep. 9 (2013), no. 4, 2889–2891. arXiv
    •  Jorge A. Guccione, Juan J. Guccione y Christian Valqui. A differential equation for
      polynomials related to the Jacobian conjecture.  Pro Mathematica 27 (2013) 83–98.

    2012

    • G. Carboni, J. A. Guccione, J. J. Guccione, C. Valqui, Cyclic homology of Brzezinski's crossed products and of braided Hopf crossed products, Advances in Mathematics 231 (2012) 3502–3568
    • G. Cortiñas, A. Thom. Algebraic geometry of topological spaces I.  Acta Mathematica 209 (2012) 83-131. arXiv
    • J. A. Guccione, J. J. Guccione, C. Valqui. Non commutative truncated polynomial extensions. J. Pure Appl. Algebra 216(11) 2012,  2315–2337 arXiv
    • J. A. Guccione, J. J. Guccione, C. Valqui, On the centralizers in the Weyl algebra. Proc. Amer. Math. Soc. 140 (2012), 1233-1241. arXiv
    • I. Heckenberger, A. Lochmann, L. Vendramin, Braided racks, Hurwitz  orbits and Nichols algebras with many cubic relations. Transform. Groups 17 (2012), no. 1, 157-194. arXiv
    • L. Vendramin, Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent. Proc. Amer. Math. Soc. 140 (2012), no. 11, 3715-3723. arXiv
    • L. Vendramin, On the classification of quandles of low order. J. Knot Theory Ramifications 21 (2012), no. 9, 1250088. arXiv

    2011

    • G. Carboni, J. A. Guccione, J. J. Guccione, Cohomology ring of differential operator rings, Journal of Algebra 339 (2011) 55-79
    • J. A. Guccione, J. J. Guccione, C. Valqui, Universal deformation formulas and braided module algebras, Journal of Algebra 330 (2011) 263–297
    • N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin. Pointed Hopf algebras over the sporadic simple groups, Journal of Algebra 325 (2011) pp. 305-320. arXiv.
    • N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin. The logbook of Pointed Hopf algebras over the sporadic simple groups, Journal of Algebra 325 (2011) pp. 282-304. arXiv.
    • N. Andruskiewitsch, F. Fantino, G. García, L. Vendramin, On Nichols algebras associated to simple racks. Contemp. Math. 537 (2011) 31-56. arXiv
    • N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin. Finite-dimensional pointed Hopf algebras with alternating groups are trivial. Ann. Mat. Pura Appl. (4) 190 (2011), no. 2, 225-245. arXiv
    • G. Cortiñas, C. Haesemeyer, M. E. Walker, C. Weibel.  A negative answer to a question of Bass.  Proc. Amer. Math. Soc., 139(4):1187-1200, (2011). arXiv
    • M. Graña, I. Heckenberger, L. Vendramin. Nichols algebras with many quadratic relations. Adv. Math. 227 (2011), no. 5, 1956-1989. arXiv
    • J. A. Guccione, J. J. Guccione, C. Valqui. Twisted planes. Communications in Algebra 38(5) (2010) 1930-1956. arXiv

    2010

    • N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin. Pointed Hopf algebras over some sporadic simple groups.  C. R. Math. Acad. Sci. Paris 348 (2010) pp. 605-608. arXiv.
    • N. Andruskiewitsch, F. Fantino, G. García, L. Vendramin, On twisted homogeneous racks of type D. Rev. Unión Mat. Argent. 51 2(2010) 1-16. arXiv
    • G. Carboni, J. A. Guccione, J. J. Guccione. Cyclic homology of Hopf crossed products. Advances in Mathematics, 223 (2010), 840--872.
    • G.  Cortiñas. Algebraic v. topological K-theory: a friendly match. In Topics in algebraic and topological K-theory. Springer Lecture Notes in Mathematics 2008.  arXiv
    • G. Cortiñas, C. Haesemeyer, M.E. Walker, C. Weibel. Bass' NK groups and cdh-fibrant Hochschild homology. Inventiones Mathematicae 181 (2), pp. 421-448. arXiv
    • S. Freyre, M. Graña, L. Vendramin. On Nichols algebras over PGL(2,q) and PSL(2,q). J. Algebra Appl., Vol. 9, No. 2 (2010) 195–208. arXiv

    2009

    • P. Ara, M. Brustenga, G. Cortiñas. K-theory of Leavitt path algebras.  Münster Journal of Mathematics, 2 (2009), 5--34. arXiv
    • G. Carboni, J. A. Guccione, J. J. Guccione. The cyclic homology of monogenic extensions in the noncommutative setting. Journal of Algebra 321 (2009), 404-428. arXiv.
    • G. Cortiñas, C. Haesemeyer, M. E. Walker, C. Weibel. The K-theory of toric varieties. Trans. Amer. Math. Soc. 361 (2009), 3325-3341. arXiv
    • G. Cortiñas, C. Haesemeyer, C. Weibel. Infinitesimal cohomology and the Chern character to negative cyclic homology. Math Annalen 344 (2009) 891-922. arXiv
    • G. Cortiñas, C. Weibel. Relative Chern characters for nilpotent ideals.  Algebraic Topology. The Abel Symposium 2007. Baas, N.; Friedlander, E.M.; Jahren, B.; Østvær, P.A. (Eds.). Springer, 2009; pp 61-82

    2008

    • G. Cortiñas, C. Haesemeyer, M. Schlichting, C. Weibel. Cyclic homology, cdh-cohomology and negative K-theory. Annals of Math. 167 (2008) 549-573. arXiv
    • G. Cortiñas, C. Haesemeyer, C. Weibel. K-regularity, cdh-fibrant Hochschild homology, and a conjecture of Vorst. Journal of the Amer. Math. Soc. 21 (2008), 547--561. arXiv
    • G. Cortiñas, A. Thom. Comparison between algebraic and topological K-theory of locally convex algebras. Advances in Mathematics, 218 (2008), 266-307. arXiv
    • M. Farinati, J.A. Guccione, J.J. Guccione. The cohomology of monogenic extensions in the noncommutative setting.  Journal of Algebra 319 (2008), 5101-5124. arXiv

    2007

    • G. Cortiñas, A. Thom. Bivariant algebraic K-theory. J. reine angew. Math. 510 (2007) 71-124. arXiv
    • M. Da Rocha, J. A. Guccione, J. J. Guccione. Braided module and comodule algebras, Galois extensions and elements of trace 1. Journal of Algebra 307 (2), (2007) 727-768 .
    • S. Freyre, M. Graña, L. Vendramin. On Nichols algebras over SL(2,q) and GL(2,q). J. Math. Phys. 48, 123513 (2007). arXiv.
    • M. Graña, J. J. Guccione, J. A. Guccione. Decomposition of some pointed Hopf algebras given by the canonical Nakayama automorphism J. Pure Appl. Algebra 2007 210 493-500 pdf dvi
    • M. Graña, I. Heckenberger. On a factorization of graded Hopf algebras using Lyndon words J. Algebra 2007 314 324-343 pdf dvi
    • M. Graña, J. P. Pinasco. Discrete Scale Invariance in Scale Free Graphs Physica A 2007 380 601-610 pdf
    • M. Graña, J.A. Guccione, J.J. Guccione. Decomposition of some pointed Hopf algebras given by the canonical Nakayama automorphism. Journal of Pure and
      Applied Algebra 210(2) (2007), 493-500.

    2006

    • G. Acosta, M. Graña, J. P. Pinasco. Condition numbers and scale free graphs The European Physical Journal B 2006 53 381-385 e-version pdf
    • G. Cortiñas. The obstruction to excision in K-theory and in cyclic homology. Invent. Math. 454 (2006) 143-173. arXiv
    • J. A. Guccione y J. J. Guccione. Relative cyclic homology of square zero extensions. Journal fur die reine und angewandte Mathematik 600, 51-80 (2006).

    2005

    • J.S. Carter, M. Elhamdadi, M. Graña, M. Saito Cocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology Osaka J. Math. 42 499-541 2005 ps.gz
    • C. Di Luigi, J. A. Guccione, J. J. Guccione. Brzezinski's crossed products and braided Hopf crossed products. Communications in Algebra 32, 3563-3580 (2004)
    • P. Etingof, M. Graña. Quantization of non-unitary geometric classical r-matrices Math. Res. Letters 12 2,3 141-153 2005 dvi ps.gz
    • M. Farinati. Hochschild duality, localization and smash products. Journal of Algebra. Volume 284, Issue 1, 1 (2005), 415-434. arXiv
    • M. Graña, V. Turaev. Knot theory for self-indexed graphs Trans. Amer. Math. Soc. 357 535-553 2005 dvi ps.gz djvu

    2004

    • J.L. Castiglioni, G. Cortiñas. Cosimplicial versus DG-rings: a version of the Dold-Kan correspondence. J. Pure Appl. Algebra.191 (2004) 119-142. arXiv
    • G. Cortiñas. The structure of smooth algebras in Kapranov's framework for noncommutative geometry. J. of Algebra 281 (2004) 679-694. arXiv
    • G. Cortiñas, M. de León. Cálculos efectivos de la homología cíclica negativa de hipersuperficies con singularidades aisladas. EACA 2004: Actas de los Encuentros de Algebra Computacional y Aplicaciones, 2004. L. González Vega, T. Recio (Eds.) Universidad de Cantabria. Santander, 2004.ISBN 84-688-6988-04
    • M. Farinati,  A. Solotar. G-Structure on the cohomology of Hopf algebras. Proc. Amer. Math. Soc. 132 (2004), 2859-2865. arXiv
    • M. Graña. Indecomposable racks of order p2 Beiträge Algebra Geom. 45 2 665-676 2004 dvi ps.gz
    •  Constanza Di Luigi, Jorge A. Guccione y Juan J. Guccione, Brzezinski’s crossed products and braided Hopf crossed products, Communications in Algebra 32 (2004), 3563-3580.J. A. Guccione, J.J. Guccione.

    2003

    • N. Andruskiewitsch, M. Graña. Examples of liftings of Nichols algebras over racks Téories d'homologie, repésentations et algèbres de Hopf AMA Algebra Montp. Announc. Paper 1, 6 pp. (electronic) 2003 dvi ps.gz
    • N. Andruskiewitsch, M. Graña. From racks to pointed Hopf algebras Adv. Math. 178 2 177-243 2003 ps.gz
    • G. Cortiñas, C. Valqui. Excision in bivariant periodic cyclic homology: a categorical approach. 30 (2003) 167-201. arXiv
    • G. Cortiñas. De Rham and infinitesimal cohomology in Kapranov's model for noncommutative algebraic geometry. Compositio Mathematica 136 (2003) 171-203 arXiv
    • P. Etingof, M. Graña. On rack cohomology J. Pure Appl. Algebra 177 1 49-59 2003 dvi ps.gz
    • M. Farinati. On the derived invariance of cohomology theories for coalgebras. Algebras and Representation Theory 6(3) pp. 303-331 (2003). arXiv
    • J. A. Guccione, J. J. Guccione. Hochschild cohomology of Frobenius algebras. Proceedings of the American Mathematical Society 132 (5), 1241-1250 (2003).
    • J. A. Guccione, J. J. Guccione. Theory of braided Hopf crossed products. Journal of Algebra 261 (1), 54-101 (2003)

    Articles accepted for publication


    • S. Ramírez, L. Vendramin. Decomposition theorems for involutive solutions to the Yang- Baxter equation, accepted for publication in Int. Math. Res. Not. IMRN
    • V. Lebed, L. Vendramin. Re f lection equation as a tool for studying solutions to the Yang- Baxter equation. Accepted for publication in J. Algebra

    Preprints


    • G. Arnone, Graded homotopy classification of Leavitt path algebras. arXiv
    • G. Cortiñas. Exel-Pardo algebras with a twist. arXiv
    • G. Cortiñas, M.E. Rodríguez. Simplicity of L^p-operator algebras. arXiv
    • E. Ellis, E. Rodríguez Cirone. Algebraic kk-theory and the KH-isomorphism conjecture. arXiv

    • Ö. Akgün, M. Mereb, L. Vendramin. Enumeration of set-theoretic solutions to the Yang– Baxter equation, preprint

    • M. Farinati. Universal quantum (semi)groups and Hopf envelopes, ArXiv:math/008.099370.
    • M. Farinati - J. Garcia Galofre. Universal cocycle Invariants for singular knots and links, ArXiv:math/1910.04042.
    • S. D. Corti, J. A. Guccione, J. J. Guccione. Braided Sweedler cohomology. arXiv.
    • G. Cortiñas. Cyclic homology of H-unital (pro-) algebras, Lie algebra homology of matrices, and a paper of Hanlon's. arXiv
    • G. Cortiñas, N.C. Phillips. Algebraic K-theory and properly infinite C*-algebras. arXiv
    • J. A. Guccione, J. J. Guccione. A characterization of quiver algebras based on double derivations. arXiv
    • E. Rodríguez Cirone. A strictly-functorial and small dg-enhancement of the derived category of perfect complexes. arXiv
    •  Matias Graña, Jorge A. Guccione, Juan J. Guccione. How to disentagle two braided
      Hopf algebras. Preprint ArXiv 0706.1915 (2007).
    • Jorge A. Guccione, Juan J. Guccione. A characterization of quiver algebras based on double derivations. Preprint ArXiv 0807.1148 (2008).
    • Jorge A. Guccione, Juan J. Guccione, Christian Valqui. A system of polynomial equations related to the Jacobian Conjecture. arXiv:1406.0886.
    • Jorge A. Guccione, Juan J. Guccione, Christian Valqui. The two-dimensional Jacobian conjecture and the lower side of the Newton polygon, arXiv:1605.09430.
    • Jorge A. Guccione, Juan J. Guccione, Rodrigo Horruitiner, Christian Valqui. Some algorithms related to the Jacobian Conjecture, arXiv:1708.07936.
    • Jorge A. Guccione, Juan J. Guccione, Christian Valqui. (Co)homology of crossed products in weak contexts, arXiv: 1811.02927
    • Jorge A. Guccione, Juan J. Guccione, Christian Valqui. (Co)homology of crossed products by weak Hopf algebras, arXiv:1907.05229
    • Jorge A. Guccione, Juan J. Guccione, Christian Valqui. Set-theoretic type solutions of the braid equation, arXiv:2008.13494
    • Jorge A. Guccione, Juan J. Guccione. Central extensions of some linear cycle sets. arXiv:2102.02724
    • Jorge A. Guccione, Juan J. Guccione, Christian Valqui. Cocommutative q-cycle coalgebra structures on the dual of the truncated polynomial algebra. arXiv:2107.08340

    Math Department Lecture Notes (Spanish)

  • Cursos de grado.
  • ISSN 1851-1317 (Versión Electrónica), ISSN 1851-1295 (Versión Impresa).

    • G. Cortiñas. Notas de Álgebra II. Cursos de grado, fascículo 11.  Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires.
    Cursos y Seminarios de Matemática - Serie B

    ISSN 1851-149X (Versión Electrónica), ISSN 1851-1481 (Versión Impresa)

    • G. Cortiñas. Álgebra II+1/2. Cursos y Seminarios de Matemática, Serie B, fascículo 13.  Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires.

    • M. Farinati.  Tópicos de álgebra homológica Cursos y Seminarios de Matemática, Serie B, fascículo 14.  Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires.

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