English

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

R2 v1 2026-06-23T06:20:32.959Z