Rank Varieties for Hopf Algebras

Details Rank Varieties for Hopf Algebras Rank Varieties for Hopf Algebras

2009-06-23

arxiv.org/abs/0906.4213v2

Mathematics

Representation Theory

13 pages, submitted

Scientific paper

We construct rank varieties for the Drinfel'd double of the Taft algebra and for U_q(sl2). For the Drinfel'd double when n=2 this uses a result which identifies a family of subalgebras that control projectivity of A-modules whenever A is a Hopf algebra satisfying a certain homological condition. In this case we show that our rank variety is homeomorphic to the cohomological support variety. We also show that Ext^*(M,M) is finitely generated over the cohomology ring of the Drinfel'd double for any finitely-generated module M.

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