☆ 4.2 Article

On the Galois symmetries for the character table of an integral fusion category

JOURNAL OF ALGEBRA AND ITS APPLICATIONS (2023)

The applications of probability groups on Hopf algebras

Jingheng Zhou et al.

Summary: In this work, probability groups are used to study a semisimple Hopf algebra H with a commutative character ring. It is proven that the algebra generalized by the dual probability group is the center Z(H) of H, and the product of two class sums is an integral combination up to a factor of dim(H)(-1) of the class sums of H. All 2-integral probability groups with two or three elements are classified.

COMMUNICATIONS IN ALGEBRA (2021)

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Article Mathematics

Structure constants for premodular categories

Sebastian Burciu

Summary: This paper studies conjugacy classes for pivotal fusion categories and proves a Burnside type formula for the structure constants concerning the product of two conjugacy class sums of such a fusion category. It also shows that for a braided weakly integral fusion category, these structure constants multiplied by dim(C) are non-negative integers, expanding on previous results in the settings of semisimple quasitriangular Hopf algebras by Zhou and Zhu.

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY (2021)

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Article Mathematics, Applied