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
Recommended Citation
Jörg Feldvoss, Sarah Witherspoon, Support Varieties and Representation Type of Small Quantum Groups, International Mathematics Research Notices, Volume 2010, Issue 7, 2010, Pages 1346–1362, https://doi.org/10.1093/imrn/rnp189
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.