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Examples of support varieties for Hopf algebras with noncommutative tensor products

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Abstract

The representations of some Hopf algebras have curious behavior: Nonprojective modules may have projective tensor powers, and the variety of a tensor product of modules may not be contained in the intersection of their varieties. We explain a family of examples of such Hopf algebras and their modules, and classify left, right, and two-sided ideals in their stable module categories.

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Authors and Affiliations

  1. Institute of Mathematics, King’s College, University of Aberdeen, Aberdeen, AB24 3UE, Scotland, UK

    Dave Benson

  2. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

    Sarah Witherspoon

Authors
  1. Dave Benson
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  2. Sarah Witherspoon
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Correspondence to Dave Benson.

Additional information

This material is based upon work supported by the National Science Foundation under Grant No. 0932078 000, while the authors were in residence at the Mathematical Science Research Institute (MSRI) in Berkeley, California, during the Spring semester of 2013. The second author was supported by National Science Foundation Grant No. DMS-1101399.

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Benson, D., Witherspoon, S. Examples of support varieties for Hopf algebras with noncommutative tensor products. Arch. Math. 102, 513–520 (2014). https://doi.org/10.1007/s00013-014-0659-8

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  • DOI: https://doi.org/10.1007/s00013-014-0659-8

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