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Tensor ideals and varieties for modules of quantum elementary abelian groups


Authors: Julia Pevtsova and Sarah Witherspoon
Journal: Proc. Amer. Math. Soc. 143 (2015), 3727-3741
MSC (2010): Primary 16E40, 16T05, 18D10
DOI: https://doi.org/10.1090/proc/12524
Published electronically: April 6, 2015
MathSciNet review: 3359565
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Abstract: In a previous paper 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.


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Additional Information

Julia Pevtsova
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: julia@math.washington.edu

Sarah Witherspoon
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: sjw@math.tamu.edu

DOI: https://doi.org/10.1090/proc/12524
Keywords: Support variety, rank variety, elementary abelian group, tensor product property, tensor ideal
Received by editor(s): December 18, 2013
Received by editor(s) in revised form: April 11, 2014
Published electronically: April 6, 2015
Additional Notes: This material is based upon work supported by the National Science Foundation under grant No. 0932078000, while the second author was in residence at the Mathematical Sciences Research Institute (MSRI) in Berkeley, California, during the semester of Spring 2013. The first author was supported by NSF grant DMS-0953011, and the second author by NSF grant DMS-1101399.
Communicated by: Kailash Misra
Article copyright: © Copyright 2015 American Mathematical Society