Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation
Rings and Algebras
2023-10-13 v3 Group Theory
Quantum Algebra
Abstract
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, we consider annihilator nilpotent skew braces, an important class that turns out to be a brace-theoretic analog to the class of nilpotent groups. In this vein, several well-known theorems in group theory are proved in the more general setting of skew braces.
Keywords
Cite
@article{arxiv.2205.01572,
title = {Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation},
author = {E. Jespers and A. Van Antwerpen and L. Vendramin},
journal= {arXiv preprint arXiv:2205.01572},
year = {2023}
}
Comments
18 pages. In this version, Definition 5.5 and Proposition 5.6 were modified following arXiv:2310.07474. Postprint version