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Structure constants for premodular categories
Author(s) -
Burciu Sebastian
Publication year - 2021
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12459
Subject(s) - mathematics , conjugacy class , quasitriangular hopf algebra , pure mathematics , class (philosophy) , product (mathematics) , fusion rules , fusion , constant (computer programming) , hopf algebra , algebra over a field , geometry , linguistics , artificial intelligence , computer science , image fusion , philosophy , cellular algebra , programming language , algebra representation
In this paper, we study conjugacy classes for pivotal fusion categories. In particular, we prove a Burnside type formula for the structure constants concerning the product of two conjugacy class sums of such a fusion category. For a braided weakly integral fusion category C , we show that these structure constants multiplied by dim ( C ) are non‐negative integers, extending some results obtained by Zhou and Zhu (see Preprint, 2019, arXiv:1912.07831v1) in the settings of semisimple quasitriangular Hopf algebras.
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