Support varieties and representation type of self-injective algebras. (Q650987)

The authors obtain a wildness criterion for self-injective algebras using Hochschild cohomology and the theory of support varieties. This is a slightly weaker version of the criterion of \textit{P. A. Bergh} and \textit{Ø. Solberg}, [Q. J. Math. 61, No. 2, 171-182 (2010; Zbl 1238.16003)]. Most of the article is devoted to applications: the authors apply the theory to Hecke algebras, reduced enveloping algebras of restricted Lie algebras, small half-quantum groups and Nichols quantum symmetric algebras. The authors also show that for a Hopf algebra one may make a choice so that the support varieties for a module defined in terms of Hochschild cohomology are isomorphic to support varieties defined in terms of the cohomology ring of the Hopf algebra. This gives a direct connection between these two different theories on support varieties for Hopf algebras.