English

The Picard crossed module of a braided tensor category

Quantum Algebra 2012-02-02 v1 Category Theory

Abstract

For a finite braided tensor category we introduce its Picard crossed module consisting of the group of invertible module categories and the group of braided tensor autoequivalences. We describe the Picard crossed module in terms of braided autoequivalences of the Drinfeld center of the braided tensor category. As an illustration, we compute the Picard crossed module of a braided pointed fusion category.

Keywords

Cite

@article{arxiv.1202.0061,
  title  = {The Picard crossed module of a braided tensor category},
  author = {Alexei Davydov and Dmitri Nikshych},
  journal= {arXiv preprint arXiv:1202.0061},
  year   = {2012}
}