Hopf-Frobenius Algebras and a Simpler Drinfeld Double
نویسندگان
چکیده
منابع مشابه
A Frobenius-Schur theorem for Hopf algebras
In this note we prove a generalization of the Frobenius-Schur theorem for finite groups for the case of semisimple Hopf algebra over an algebraically closed field of characteristic 0. A similar result holds in characteristic p > 2 if the Hopf algebra is also cosemisimple. In fact we show a more general version for any finite-dimensional semisimple algebra with an involution; this more general r...
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The classical Frobenius–Schur indicators for finite groups are character sums defined for any representation and any integer m ≥ 2. In the familiar case m = 2, the Frobenius–Schur indicator partitions the irreducible representations over the complex numbers into real, complex, and quaternionic representations. In recent years, several generalizations of these invariants have been introduced. Bu...
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This expository article presents a unified ring theoretic approach, based on the theory of Frobenius algebras, to a variety of results on Hopf algebras. These include a theorem of S. Zhu on the degrees of irreducible representations, the so-called class equation, the determination of the semisimplicity locus of the Grothendieck ring, the spectrum of the adjoint class and a non-vanishing result ...
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Classically, the exponent of a group is the least common multiple of the orders of its elements. This notion was generalized by Etingof and Gelaki to the context of Hopf algebras. Kashina, Sommerhäuser and Zhu later observed that there is a strong connection between exponents and Frobenius– Schur indicators. In this paper, we introduce the notion of twisted exponents and show that there is a si...
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Mason and Ng have given a generalization to semisimple quasiHopf algebras of Linchenko and Montgomery’s generalization to semisimple Hopf algebras of the classical Frobenius-Schur theorem for group representations. We give a simplified proof, in particular a somewhat conceptual derivation of the appropriate form of the Frobenius-Schur indicator that indicates if and in which of two possible fas...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2020
ISSN: 2075-2180
DOI: 10.4204/eptcs.318.10