Some applications of Frobenius algebras to Hopf algebras

Publication status: In: Groups, Algebras and Applications, Contemporary Mathematics, vol. 537, Amer. Math. Soc., Providence, RI, 2011, pp. 269-289.
arXiv: http://arxiv.org/abs/1008.4054

Abstract: 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 the so-called class equation, the determination of the semisimplicity locus of the Grothendieck ring, and a non-vanishing result for the adjoint character.

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