Document Type

Article

Publication Title

International Mathematics Research Notices

Abstract

In this paper, we provide a wildness criterion for any finite dimensional Hopf algebra with finitely generated cohomology. This generalizes a result of Farnsteiner to not necessarily cocommutative Hopf algebras over ground fields of arbitrary characteristic. Our proof uses the theory of support varieties for modules, one of the crucial ingredients being a tensor product property for some special modules. As an application, we prove a conjecture of Cibils stating that small quantum groups of rank at least two are wild.

First Page

1346

Last Page

1362

DOI

https://doi.org/10.1093/imrn/rnp189

Publication Date

2010

Department

Mathematics and Statistics

Comments

This is the pre-print version for this article. The published version can be found in the journal International Mathematics Research Notices at this link: https://academic.oup.com/imrn/article/2010/7/1346/651735.

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