Leandro Vendramin’s publication list

Preprints

Algebra with GAP (with K. Piterman).

Accepted for publication

The prime spectrum of an L-algebra (with W. Rump). Proc. Amer. Math. Soc.
On computing finite index subgroups of PSL(2,Z) (with N. Mayorga Uruburu, A. Pacetti). J. Algebra Appl.
Skew braces: a brief survey. Geometric methods in physics XL. Trends Math.

2024

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.
What is… a skew brace? Notices Amer. Math. Soc. 71 (2024), no. 1, 65-67.
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.
Mini-workshop: Skew braces and the Yang-Baxter equation (with T. Brzezinski, I. Colazzo, A. Doikou). Oberwolfach Rep. 20 (2023), no. 1, 537-563.
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

Nudos, quandles y homología (Spanish). Gac. R. Soc. Mat. Esp. 25 (2022), no. 1, 85-110. [GitHub].
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.
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).

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.
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.

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.

2013

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]

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

On Nichols algebras associated to simple racks (with N. Andruskiewitsch, F. Fantino, G. García). Groups, Algebras and Applications, Contemp. Math. 537 (2011) 31-56.
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

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.
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).