Rank Varieties for Hopf Algebras

2009/06/23 by Matthew Towers, Towers, Matthew, Sarah Scherotzke +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.0906.4213

13 pages, submitted

openalex publication_date 2009/06/23 · arxiv created 2009/06/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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