Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications Article Swipe
Related Concepts
Mathematics
Brauer group
Bimodule
Hopf algebra
Picard group
Pure mathematics
Invertible matrix
Group (periodic table)
Algebra over a field
Brauer's theorem on induced characters
Quantum group
Crossed product
Organic chemistry
Chemistry
Simon Lentner
,
Jan Priel
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.36045/bbms/1489888815
· OA: W2596983849
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.36045/bbms/1489888815
· OA: W2596983849
In this article we construct three explicit natural subgroups of the\nBrauer-Picard group of the category of representations of a\nfinite-dimensional Hopf algebra. In examples the Brauer Picard group decomposes\ninto an ordered product of these subgroups, somewhat similar to a Bruhat\ndecomposition.\nOur construction returns for any Hopf algebra three types of braided\nautoequivalences and correspondingly three families of invertible bimodule\ncategories. This gives examples of so-called (2-)Morita\nequivalences and defects in topological field theories. We have a closer\nlook at the case of quantum groups and Nichols algebras and give\ninteresting applications. Finally, we briefly discuss the three families of\ngroup-theoretic extensions.
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