Some applications of Frobenius algebras to Hopf algebras

Details Some applications of Frobenius algebras to Hopf algebras Some applications of Frobenius algebras to Hopf algebras

2010-08-24

arxiv.org/abs/1008.4054v1

Mathematics

Rings and Algebras

22 pages

Scientific paper

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 for the adjoint character.

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