Leandro Vendramin

Leandro Vendramin’s publication list

Click here for a selection of papers.

Preprints

• Rubik’s as a Galois’ (with M. Mereb).
• Pointed Hopf algebras of odd dimension and Nichols algebras over solvable groups (with N. Andruskiewitsch, I. Heckenberger).
• Hopf formulae for homology of skew braces (with M. Gran, T. Letourmy).
• Algebra with GAP (with K. Piterman).

Accepted for publication

• On computing finite index subgroups of PSL(2,Z) (with N. Mayorga Uruburu, A. Pacetti). J. Algebra Appl.

Published papers

2024

• Skew braces: a brief survey. Geometric methods in physics XL, workshop, Białowieża, Poland, June 20-25, 2023. Cham: Birkhäuser. 153-175.
• The prime spectrum of an L-algebra (with W. Rump). Proc. Amer. Math. Soc. 152 (2024), 3197-3207.
• Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension (with I. Heckenberger, E. Meir). Adv. Math. 444 (2024), Paper No. 109637.
• Involutive Yang-Baxter: cabling, decomposability, Dehornoy class (with V. Lebed, S. Ramírez). Rev. Mat. Iberoam. 40 (2024), no. 2, pp. 623–635.
• Schur covers of skew braces (with T. Letourmy) J. Algebra 644 (2024), 609-654.

2023

• Bosonization of curved Lie bialgebras (with I. Heckenberger). Bull. Belg. Math. Soc. Simon Stevin 30 (2023), no. 5, 577–600.
• Isoclinism of skew braces (with T. Letourmy). Bull. Lond. Math. Soc. 55 (2023), no. 6, 2891–2906.
• Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation (with E. Jespers, A. Van Antwerpen). Commun. Contemp. Math. 25 (2023), no. 09, Paper No. 2250064.
• On the enumeration of finite L-algebras (with C. Dietzel, P. Menchón). Math. Comp. 92 (2023), no. 341, 1363–1381 [code].

2022

• Decomposition theorems for involutive solutions to the Yang-Baxter equation (with S. Ramírez). Int. Math. Res. Not. IMRN 2022, no. 22, 18078–18091.
• Reflection equation as a tool for studying solutions to the Yang-Baxter equation (with V. Lebed). J. Algebra 607 (2022), 360–380.
• Enumeration of set-theoretic solutions to the Yang-Baxter equation (with Ö. Akgün, M. Mereb). Math. Comp. 91 (2022), no. 335, 1469–1481 [code].

2021

• Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation (with E. Jespers, L. Kubat, A. Van Antwerpen). Adv. Math. 385 (2021), 107767.
• On skew braces and their ideals (with O. Konovalov, A. Smoktunowicz). Exp. Math. 30 (2021), no. 1, 95–104, errata.

2020

• Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces (with E. Acri, R. Lutowski). Internat. J. Algebra Comput. 30 (2020), no. 1, 91–115.
• Combinatorial solutions to the reflection equation (with A. Smoktunowicz, R. Weston). J. Algebra 549 (2020) 268-290.

2019

• Factorization of skew braces (with E. Jespers, L. Kubat, A. Van Antwerpen). Math. Ann. 375 (2019), no. 3-4, 1649–1663.
• PBW deformations of a Fomin-Kirillov algebra and other examples (with I. Heckenberger). Algebr. Represent. Theory 22 (2019), no. 6, 1513–1532.
• Skew left braces of nilpotent type (with F. Cedó, A. Smoktunowicz). Proc. Lond. Math. Soc. (3) 118 (2019), no. 6, 1367-1392.
• On structure groups of set-theoretic solutions to the Yang-Baxter equation (with V. Lebed). Proc. Edinb. Math. Soc. (2) 62 (2019), no. 3, 683-717.
• Problems on skew left braces. Adv. Group Theory Appl. 7 (2019), 15-37.

2018

• A characterization of multipermutation solutions of the Yang-Baxter equation (with D. Bachiller and F. Cedó). Publ. Mat. 62 (2018), no. 2, 641-649.
• Yang-Baxter operators in symmetric categories (with J. Guccione and J. Guccione). Comm. Algebra 46 (2018), no. 7, 2811–2845.
• On skew braces (with an appendix by N. Byott) (with A. Smoktunowicz). J. Comb. Algebra 2 (2018), no. 1, 47–86.

2017

• Doubly transitive groups and cyclic quandles. J. Math. Soc. Japan 69 (2017), no. 3, 1051–1057.
• An explicit description of the second cohomology group of a quandle (with A. García Iglesias). Math. Z. 286 (2017), no. 3-4, 1041-1063.
• The classification of Nichols algebras with finite root system of rank two (with I. Heckenberger). J. Eur. Math. Soc. (JEMS) 19 (2017), no. 7, 1977–2017.
• Skew braces and the Yang-Baxter equation (with L. Guarnieri). Math. Comp. 86 (2017), no. 307, 2519–2534.
• Hopf braces and Yang-Baxter operators (with I. Angiono, C. Galindo). Proc. Amer. Math. Soc. 145 (2017), no. 5, 1981-1995.
• A classification of Nichols algebras of semi-simple Yetter-Drinfeld modules over non-abelian groups (with I. Heckenberger). J. Eur. Math. Soc. (JEMS) 19 (2017), no. 2, 299-356.
• Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation (with V. Lebed). Adv. Math. 304 (2017), 1219-1261.

2016

• Cohomology and extensions of braces (with V. Lebed). Pacific J. Math. 284 (2016), no. 1, 191-212.
• Quandle coloring and cocycle invariants of composite knots and abelian extensions (with W. E. Clark, M. Saito). J. Knot Theory Ramifications 25 (2016), no. 5, 1650024, 34 pp..
• Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova. J. Pure Appl. Alg. 220 (2016), no. 5, 2064-2076.

2015

• Nichols algebras with many cubic relations (with I. Heckenberger, A. Lochmann). Trans. Amer. Math. Soc. 367 (2015), no. 9, 6315-6356.
• Nichols algebras over groups with finite root system of rank two III (with. I. Heckenberger). J. Algebra 422 (2015), 223–256.
• Frobenius property for fusion categories of small integral dimension (with J. Dong, S. Natale). J. Algebra Appl. 14 (2015), no. 2, 1550011 (17 pages).

2014

• Nichols algebras over groups with finite root system of rank two II (with I. Heckenberger). J. Group Theory 17 (2014), no. 6, 1009-1034.

2012

• Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent. Proc. Amer. Math. Soc. 140 (2012), no. 11, 3715-3723.
• On the classification of quandles of low order. J. Knot Theory Ramifications 21 (2012), no. 9, 1250088.
• Braided racks, Hurwitz actions and Nichols algebras with many cubic relations (with I. Heckenberger, A. Lochmann). Transform. Groups 17 (2012), no. 1, 157-194.

2011

• Nichols algebras of group type with many quadratic relations (with M. Graña, I. Heckenberger). Adv. Math. 227 (2011), no. 5, 1956-1989.
• Pointed Hopf algebras over the sporadic simple groups (with N. Andruskiewitsch, F. Fantino, M. Graña). J. Algebra 325 (2011) 305-320. [logs]
• The logbook of Pointed Hopf algebras over the sporadic simple groups (with N. Andruskiewitsch, F. Fantino, M. Graña). J. Algebra 325 (2011) 282-304.
• Finite-dimensional pointed Hopf algebras with alternating groups are trivial (with N. Andruskiewitsch, F. Fantino, M. Graña). Ann. Mat. Pura Appl. (4) 190 (2011), no. 2, 225-245.

2010

• Pointed Hopf algebras over some sporadic simple groups (with N. Andruskiewitsch, F. Fantino, M. Graña). C. R. Math. Acad. Sci. Paris 348 (2010) 605-608.
• On Nichols algebras over PGL(2,q) and PSL(2,q) (with S. Freyre, M. Graña). J. Algebra Appl., Vol. 9, No. 2 (2010) 195-208. [logs]

2007

• On Nichols algebras over SL(2,q) and GL(2,q) (with S. Freyre, M. Graña). J. Math. Phys. 48, 123513 (2007).

Conference proceedings, reports and other publications

• Mini-workshop:Bridging number theory and Nichols algebras via deformations (With G. Carnovale, I. Heckenberger). Oberwolfach Rep. 21, No. 1, 235-272 (2024).
• What is… a skew brace? Notices Amer. Math. Soc. 71 (2024), no. 1, 65-67.
• Nudos, quandles y homología (Spanish). Gac. R. Soc. Mat. Esp. 25 (2022), no. 1, 85-110. [GitHub].
• Mini-workshop: Skew braces and the Yang-Baxter equation (with T. Brzezinski, I. Colazzo, A. Doikou). Oberwolfach Rep. 20 (2023), no. 1, 537-563.
• Quantum invariants via Hopf algebras and solutions to the Yang-Baxter equation. Adams, Colin (ed.), Flapan, Erica (ed.); Henrich, Allison (ed.); Kauffman, Louis H. (ed.); Ludwig, Lewis D. (ed.); Nelson, Sam (ed.) Encyclopedia of knot theory. Boca Raton, FL: CRC Press. 795-800 (2021).
• Mini-workshop: Algebraic tools for solving the Yang-Baxter equation. Abstracts from the mini-workshop held November 10–16, 2019 (with E. Jespers, V. Lebed, W. Rump). Oberwolfach Rep. 16 (2020), no. 4, 3207-3242.
• Fomin-Kirillov algebras. Nichols algebras and Weyl groupoids, Oberwolfach Rep. 9 (2013), no. 4, 2889–2891.
• On twisted conjugacy classes of type D in sporadic simple groups (with F. Fantino). Hopf Algebras and Tensor Categories, Contemp. Math. 585 (2013) 247-259. [logs]
• On Nichols algebras associated to simple racks (with N. Andruskiewitsch, F. Fantino, G. García). Groups, Algebras and Applications, Contemp. Math. 537 (2011) 31-56.
• On twisted homogeneous racks of type D (with N. Andruskiewitsch, F. Fantino, G. García). The Humboldt Kolleg Colloquium on Hopf Algebras, Quantum Groups and Tensor Categories, Rev. Un. Mat. Argentina 51 2(2010) 1-16.