Support Varieties and Representation Type of Small Quantum Groups
- 8 December 2009
- journal article
- research article
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2010 (7) , 1346-1362
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.Keywords
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