Bulletin of the Belgian Mathematical Society - Simon Stevin

Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications

Simon Lentner and Jan Priel

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Abstract

In this article we construct three explicit natural subgroups of the Brauer-Picard group of the category of representations of a finite-dimensional Hopf algebra. In examples the Brauer Picard group decomposes into an ordered product of these subgroups, somewhat similar to a Bruhat decomposition. Our construction returns for any Hopf algebra three types of braided autoequivalences and correspondingly three families of invertible bimodule categories. This gives examples of so-called (2-)Morita equivalences and defects in topological field theories. We have a closer look at the case of quantum groups and Nichols algebras and give interesting applications. Finally, we briefly discuss the three families of group-theoretic extensions.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 1 (2017), 73-106.

Dates
First available in Project Euclid: 19 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1489888815

Digital Object Identifier
doi:10.36045/bbms/1489888815

Mathematical Reviews number (MathSciNet)
MR3625786

Zentralblatt MATH identifier
06751308

Subjects
Primary: 16T05: Hopf algebras and their applications [See also 16S40, 57T05]

Keywords
Brauer-Picard group Module categories Hopf algebra

Citation

Lentner, Simon; Priel, Jan. Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 1, 73--106. doi:10.36045/bbms/1489888815. https://projecteuclid.org/euclid.bbms/1489888815


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