The Picard crossed module of a braided tensor category

By Alexei Davydov, D. Nikshych. 2012

68 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/af6a5c35bda3b3cf16a743855216709d0ccbde06

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Christopher J. Schommer-Pries
2. Noah Snyder
3. Christopher L. Douglas
4. Bai-Ling Wang
5. Jon P. May
6. J. Sigurdsson
7. D. Nikshych
8. Alexei Davydov

In Geometry and Topology

1. Christopher J. Schommer-Pries
2. Noah Snyder
3. Christopher L. Douglas
4. Bai-Ling Wang
5. Clark Barwick
6. J. Sigurdsson
7. Alexei Davydov
8. Jon P. May

In Mathematical Physics

1. Christopher J. Schommer-Pries
2. Noah Snyder
3. Christopher L. Douglas
4. Bai-Ling Wang
5. E. Sharpe
6. Clark Barwick
7. J. Sigurdsson
8. Jon P. May

Citations in the corpus

• The balanced tensor product of module categories (2014, background): “ satisfying the additional assumption that M Nis exact as a C-bimodule category can be extracted from [Gre11, Thm 3.1]. Note that the proof of the existence of the balanced tensor product outlined in [DN13] uses the rigidity and niteness assumptions in essential ways, but (despite [DN13, Note 2.7]) ”