Braided Picard groups and graded extensions of braided tensor categories
Abstract
We classify various types of graded extensions of a finite braided tensor category $\cal B$ in terms of its $2$categorical Picard groups. In particular, we prove that braided extensions of $\cal B$ by a finite group $A$ correspond to braided monoidal $2$functors from $A$ to the braided $2$categorical Picard group of $\cal B$ (consisting of invertible central $\cal B$module categories). Such functors can be expressed in terms of the EilnbergMac~Lane cohomology. We describe in detail braided $2$categorical Picard groups of symmetric fusion categories and of pointed braided fusion categories.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.08022
 Bibcode:
 2020arXiv200608022D
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Category Theory