Hopf algebra actions in tensor categories
Quantum Algebra
2020-06-01 v2 Mathematical Physics
Category Theory
math.MP
Abstract
We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action allows us to see the algebra as the regular algebra in the representation category of the acting group.
Keywords
Cite
@article{arxiv.1811.10528,
title = {Hopf algebra actions in tensor categories},
author = {Marcel Bischoff and Alexei Davydov},
journal= {arXiv preprint arXiv:1811.10528},
year = {2020}
}
Comments
8pages, several figures. v2 minor changes. As sent for publication to Transformation Groups