Set-theoretic type solutions of the braid equation
Rings and Algebras
2024-11-01 v5
Abstract
In this paper we begin the study of set-theoretic type solution of the braid equation. Our theory includes set-theoretical solutions as basic examples. We show that the relationships between set-theoretical solutions, q-cycle sets, q-braces, skew-braces, matched pairs of groups and invertible -cocycles remain valid in our setting.
Cite
@article{arxiv.2008.13494,
title = {Set-theoretic type solutions of the braid equation},
author = {Jorge A. Guccione and Juan J. Guccione and Christian Valqui},
journal= {arXiv preprint arXiv:2008.13494},
year = {2024}
}
Comments
41 pages. We change the already published paper. In Theorem 5.17 we adapt Theorem 1 of [21] to the context of Hopf algebras. We rewrite part of sections 5 and 6, dropping in several places the requirement that the antipode S of H be bijective. In Subsection 6.2, we show that the category of Hopf skew braces is isomorphic to the category of Yetter-Drinfeld braces, recently introduced in [10]