English

Fusion rules of equivariantizations of fusion categories

Quantum Algebra 2019-10-18 v2 Representation Theory

Abstract

We determine the fusion rules of the equivariantization of a fusion category C\mathcal{C} under the action of a finite group GG in terms of the fusion rules of C\mathcal{C} and group-theoretical data associated to the group action. As an application we obtain a formula for the fusion rules in an equivariantization of a pointed fusion category in terms of group-theoretical data. This entails a description of the fusion rules in any braided group-theoretical fusion category.

Keywords

Cite

@article{arxiv.1206.6625,
  title  = {Fusion rules of equivariantizations of fusion categories},
  author = {Sebastian Burciu and Sonia Natale},
  journal= {arXiv preprint arXiv:1206.6625},
  year   = {2019}
}

Comments

The assumption that the group action is by tensor autoequivalences on a fusion category was added in Section 2. Modified statements of Proposition 6.2, Corollary 2.13. Statements of Propositions 3.12 and Corollary 3.13 modified accordingly