Invariants and semi-direct products for finite group actions on tensor categories. (English) Zbl 0980.18003

Tambara, Daisuke

J. Math. Soc. Japan 53, No. 2, 429-456 (2001).

Given an action of a finite group on a tensor category, we form two tensor categories. One is the category of group invariant objects of the tensor category, and the other is the semi-direct product of the group and the tensor category. We show that if the characteristic of the base field does not divide the order of the group, there exists a one-to-one correspondence between linear categories with action of these two tensor categories.

Reviewer: D.Tambara

MSC:

18D10	Monoidal, symmetric monoidal and braided categories (MSC2010)
20J06	Cohomology of groups
18D05	Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)

Keywords:

group action; Morita equivalence; 3-cocycle; tensor categories; linear categories