287 citations · 1.4k across the 60 of their papers we have counts for
63 papers
Higher Fomin-Kirillov algebras are infinite-dimensional
N. Andruskiewitsch, I. Angiono, I. Heckenberger +3
We show that the Fomin--Kirillov algebras are infinite-dimensional for . This answers a question posed by Fomin and Kirillov in 1997. To prove this, we demonstrate t…
The Köthe conjecture via point modules
B. Greenfeld, B. King, L. Vendramin
We give a short construction refuting the Köthe Conjecture. The construction is based on the point module approach to the problem, introduced by the first-named and second-named au…
On Noetherian pointed Hopf algebras
N. Andruskiewitsch, I. Heckenberger, L. Vendramin
In arXiv:1405.4105 it was asked whether an affine Hopf algebra with finite Gelfand-Kirillov dimension is necessarily Noetherian. It is well-known that the converse is not true --ta…
Point modules of Nichols algebras over non-abelian groups
B. Greenfeld, L. Vendramin, S. Venkatesh
Nichols algebras are among the most important and mysterious objects in quantum algebra. We continue the systematic program of studying them through their point modules. We study t…
Galois' Professor's Revenge
M. Damele, A. Loi, M. Mereb +1
We prove that the groups associated with the Revenge Cube and the Professor's Cube can be realized as Galois groups over the rationals.
Computing finite Weyl groupoids
Iván Angiono, Leandro Vendramin
We present algorithms to compute generalized root systems of Nichols algebras of diagonal type and of contragredient Lie superalgebras. As a consequence, we obtain an algorithm to…
Incremental SAT-Based Enumeration of Solutions to the Yang-Baxter Equation
Daimy Van Caudenberg, Bart Bogaerts, Leandro Vendramin
We tackle the problem of enumerating set-theoretic solutions to the Yang-Baxter equation. This equation originates from statistical and quantum mechanics, but also has applications…
Pointed Hopf algebras of odd dimension and Nichols algebras over solvable groups
N. Andruskiewitsch, I. Heckenberger, L. Vendramin
We classify finite-dimensional Nichols algebras of Yetter-Drinfeld modules with indecomposable support over finite solvable groups in characteristic 0, using a variety of methods i…
Rubik's as a Galois'
M. Mereb, L. Vendramin
We prove that the Rubik's cube group can be realized as a Galois group over the rationals.
Hopf formulae for homology of skew braces
M. Gran, T. Letourmy, L. Vendramin
The variety of skew braces contains several interesting subcategories as subvarieties, as for instance the varieties of radical rings, of groups and of abelian groups. In this arti…
Skew braces: a brief survey
Leandro Vendramin
Our primary focus is on the theory of skew braces, specifically exploring their connection with combinatorial solutions to the Yang-Baxter equation. Skew braces have recently emerg…
On computing finite index subgroups of PSL(2,Z)
Nicolás Mayorga Uruburu, Ariel Pacetti, Leandro Vendramin
We present a method to compute finite index subgroups of . Our strategy follows Kulkarni's ideas, the main contribution being a recursive method to compute bival…
Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension
I. Heckenberger, E. Meir, L. Vendramin
Over fields of characteristic zero, we determine all absolutely irreducible Yetter-Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols alg…
Schur covers of skew braces
T. Letourmy, L. Vendramin
We develop the theory of Schur covers of finite skew braces. We prove the existence of at least one Schur cover. We also compute several examples. We prove that different Schur cov…
Isoclinism of skew braces
Thomas Letourmy, Leandro Vendramin
We define isoclinism of skew braces and present several applications. We study some properties of skew braces that are invariant under isoclinism. For example, we prove that right…
Bosonization of curved Lie bialgebras
I. Heckenberger, L. Vendramin
We use Cartier's preadditive symmetric monoidal categories to study Lie bialgebras. We prove that bosonization can be done consistently in this framework. In the last part of the p…
Involutive Yang-Baxter: cabling, decomposability, Dehornoy class
V. Lebed, S. Ramírez, L. Vendramin
We develop new machinery for producing decomposability tests for involutive solutions to the Yang-Baxter equation. It is based on the seminal decomposability theorem of Rump, and o…
On the enumeration of finite -algebras
C. Dietzel, P. Menchón, L. Vendramin
We use Constraint Satisfaction Methods to construct and enumerate finite -algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory…
The prime spectrum of an -algebra
W. Rump, L. Vendramin
We prove that the lattice of ideals of an arbitrary -algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. t…
Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation
E. Jespers, A. Van Antwerpen, L. Vendramin
We study relations between different notions of nilpotency in the context of skew braces and applications to the structure of solutions to the Yang-Baxter equation. In particular,…
Decomposition theorems for involutive solutions to the Yang-Baxter equation
S. Ramírez, L. Vendramin
Motivated by the proof of Rump of a conjecture of Gateva-Ivanova on the decomposability of square-free solutions to the Yang-Baxter equation, we present several other decomposabili…
Enumeration of set-theoretic solutions to the Yang-Baxter equation
Ö. Akgün, M. Mereb, L. Vendramin
We use Constraint Satisfaction methods to enumerate and construct set-theoretic solutions to the Yang-Baxter equation of small size. We show that there are 321931 involutive soluti…
Reflection equation as a tool for studying solutions to the Yang-Baxter equation
V. Lebed, L. Vendramin
Given a right-non-degenerate set-theoretic solution to the Yang-Baxter equation, we construct a whole family of YBE solutions on indexed by its reflections $k…
Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation
E. Jespers, Ł. Kubat, A. Van Antwerpen +1
We define the radical and weight of a skew left brace and provide some basic properties of these notions. In particular, we obtain a Wedderburn type decomposition for Artinian skew…