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Tensor ideals and varieties for modules of quantum elementary abelian groups. (English) Zbl 1394.16038

Summary: In [Algebr. Represent. Theory 12, No. 6, 567–595 (2009; Zbl 1223.16003)], we constructed rank and support variety theories for “quantum elementary abelian groups,” that is, tensor products of copies of Taft algebras. In this paper we use both variety theories to classify the thick tensor ideals in the stable module category, and to prove a tensor product property for the support varieties.

MSC:

16T05 Hopf algebras and their applications
16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)

Citations:

Zbl 1223.16003
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References:

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