Support Varieties and Representation Type of Self-Injective Algebras
This is the pre-print version of this article. The published version can be found in the journal Homology, Homotopy and Applications, through International Press publishers at this link:
https://www.intlpress.com/site/pub/pages/journals/items/hha/content/vols/0013/0002/a013/
Abstract
We use the theory of varieties for modules arising from Hochschild cohomology to give an alternative version of the wildness criterion of Bergh and Solberg [7]: If a finite dimensional self-injective algebra has a module of complexity at least 3 and satisfies some finiteness assumptions on Hochschild cohomology, then the algebra is wild. We show directly how this is related to the analogous theory for Hopf algebras that we developed in [23]. We give applications to many different types of algebras: Hecke algebras, reduced universal enveloping algebras, small half- quantum groups, and Nichols (quantum symmetric) algebras.