### Leandro Vendramin’s publication list

Click here for a selection of papers.

#### Preprints

- 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*.