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.
Citation
Simon Lentner. Jan Priel. "Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications." Bull. Belg. Math. Soc. Simon Stevin 24 (1) 73 - 106, march 2017. https://doi.org/10.36045/bbms/1489888815
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