Some applications of Frobenius algebras to Hopf algebras
In: Groups, Algebras and Applications, Contemporary Mathematics,
vol. 537, Amer. Math. Soc., Providence, RI, 2011, pp. 269-289.
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.