Vrije Universiteit Brussel

Faculty of Sciences

Department of Mathematics and Data Science

Pleinlaan 2, B-1050

Brussel, Belgium

(+32) 2 629 3493

Email: `Leandro.Vendramin@vub.be`

CV, arXiv, MathSciNet, zbMATH, Google Scholar, ORCID

## Publications

### Preprints

- Schur covers of skew braces (with T. Letourmy).
- Isoclinism of skew braces (with T. Letourmy).
- Involutive Yang-Baxter: cabling, decomposability, Dehornoy class (with V. Lebed, S. Ramírez).
- The prime spectrum of an L-algebra (with W. Rump).

### Accepted for publication

- Bosonization of curved Lie bialgebras (with I. Heckenberger) Accepted for publication in
*Bull. Belg. Math. Soc. Simon Stevin*. - Nilpotency of skew braces and multipermutation solutions of the
Yang-Baxter equation (with E. Jespers, A. Van Antwerpen) Accepted for publication in
*Commun. Contemp. Math.*

### Published

- On the enumeration of finite L-algebras (with C. Dietzel, P. Menchón).
*Math. Comp. 92 (2023), no. 341, 1363–1381*, code. - 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. - 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. - 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*. - 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*. - 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*. - 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*. - 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*. - 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)*. - Nichols algebras over groups with finite root system of rank two II (with I. Heckenberger).
*J. Group Theory 17 (2014), no. 6, 1009-1034*. - 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*. - 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*. - 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. - On Nichols algebras over SL(2,q) and GL(2,q) (with S. Freyre, M. Graña).
*J. Math. Phys. 48, 123513 (2007)*.

### Proceedings and others

- Nudos, quandles y homología (Spanish). Gac. R. Soc. Mat. Esp. 25 (2022), no. 1, 85-110, GitHub.
- 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)*. - Some problems on skew braces and the Yang-Baxter equation. Algebraic Tools for Solving the YangBaxter Equation,
*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*.

## Lecture notes

My courses are here. Other lecture notes:

- [2023, Puerto Madryn] Algebra with GAP (notes).
- [2022, Brussels] Algebra with GAP - with Jan de Beule (slides).
- [2020, Halifax] Algebra with GAP (videos, slides and problems).
- [2015, Talca] Pecios y quandles.
- [2015, ERAG] El grupoide de Weyl.
- [2014, Rauischholzhausen] Nichols algebras.
- [2014, Santiago de Chile] Introducción al álgebra con GAP.

## My software

### Mathematics

- YangBaxter (with O. Konovalov). A GAP package for set-theoretical solutions of the YBE, braces, racks and quandles, cycle sets.
- Rig (with M. Graña). A GAP package for racks, quandles, and Nichols algebras.
- Python/Sage script for Nichols algebras and derivations.
- Sarna (with M. Graña and I. Heckenberger). Software written in Python to calculate the Arithmetic Root System associated to a braiding of diagonal type.

### Just for fun

- pysolita, simple solitaire game written in Python. Requires Pygame, screenshot.
- tetris4sdl, my own tetris game written in C. Requires SDL, screenshot.

## Links

#### Mathematics

- VUB Algebra Research Group.
- Some talks/conferences.
- Kourovka Notebook, Collection of unsolved problems in group theory.

#### Software

- Atlas of finite group representations (version 3)
- GAP System for Computational Discrete Algebra
- Magma Computational Algebra System
- OSCAR Computer Algebra System
- Sage: Open Source Mathematics Software

#### PhD Students/Postdocs

Here you find my list of PhD students and postdocs.

#### Personal homepages and coauthors

Emiliano Acri, Ögzür Akgün, Nicolás Andruskiewitsch, Iván Angiono, David Bachiler, Nigel Byott, Ferran Cedó, Edwin Clark, Carsten Dietzel, Jingcheng Dong, Fernando Fantino, César Galindo, Agustín García Iglesias, Gastón García, Matías Graña, István Heckenberger, Geoffrey Janssens, Eric Jespers, Olexandr Konovalov, Lukasz Kubat, Victoria Lebed, Thomas Letourmy, Andreas Lochmann, Rafał Lutowski, Paula Menchón, Sonia Natale, Wolfgang Rump, Masahico Saito, Agata Smoktunowicz, Arne Van Antwerpen, Robert Weston.