Frobenius-Schur Indicators for Some Fusion Categories Associated to Symmetric and Alternating Groups
نویسندگان
چکیده
منابع مشابه
Frobenius-schur Indicators for a Class of Fusion Categories
We give an explicit description, up to gauge equivalence, of group-theoretical quasi-Hopf algebras. We use this description to compute the Frobenius-Schur indicators for grouptheoretical fusion categories.
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We obtain two formulae for the higher Frobenius-Schur indicators: one for a spherical fusion category in terms of the twist of its center and the other one for a modular tensor category in terms of its twist. The first one is a categorical generalization of an analogous result by Kashina, Sommerhäuser, and Zhu for Hopf algebras, and the second one extends Bantay’s 2nd indicator formula for a co...
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We introduce the Frobenius–Schur indicator for categories with duality to give a category-theoretical understanding of various generalizations of the Frobenius–Schur theorem including that for semisimple quasi-Hopf algebras, weak Hopf C∗-algebras and association schemes. Our framework also clarifies a mechanism of how the “twisted” theory arises from the ordinary case. As a demonstration, we es...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2016
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-016-9593-8