Conjugacy classes and centralizers for pivotal fusion categories

Conjugacy classes and centralizers for pivotal fusion categories

A criterion for the Müger centralizer of a fusion subcategory of a braided non-degenerate fusion category is given. Along the way we extend some identities on the space of class functions of a fusion category introduced by Shimizu (J Pure Appl Algebra 221(9):2338–2371, 2017). We also show that in a...

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Veröffentlicht in:Monatshefte für Mathematik 2020-09, Vol.193 (1), p.13-46
1. Verfasser: Burciu, Sebastian
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description A criterion for the Müger centralizer of a fusion subcategory of a braided non-degenerate fusion category is given. Along the way we extend some identities on the space of class functions of a fusion category introduced by Shimizu (J Pure Appl Algebra 221(9):2338–2371, 2017). We also show that in a modular tensor category the product of two conjugacy class sums is a linear combination of conjugacy class sums with rational coefficients.
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subjects Algebra
Categories
Mathematical analysis
Mathematics
Mathematics and Statistics
Oil field equipment
Sums
Tensors
title Conjugacy classes and centralizers for pivotal fusion categories
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