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PIMS Summer School and Workshop

PSSW 2016: Geometric and Topological Aspects of the Representation Theory of Finite Groups pp 481–495Cite as

Varieties for Modules of Finite Dimensional Hopf Algebras

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 242))

Abstract

We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples such as finite group algebras and finite group schemes. We list open questions about tensor products of modules and projectivity, where varieties may play a role in finding answers.

Dedicated to Professor David J. Benson on the occasion of his 60th birthday

The author was partially supported by NSF grant #DMS-1401016.

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Author information

Authors and Affiliations

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

    Sarah Witherspoon

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  1. Sarah Witherspoon
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Correspondence to Sarah Witherspoon .

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Editors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, USA

    Jon F. Carlson

  2. Department of Mathematics, University of Utah, Salt Lake City, UT, USA

    Srikanth B. Iyengar

  3. Department of Mathematics, University of Washington, Seattle, WA, USA

    Julia Pevtsova

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Witherspoon, S. (2018). Varieties for Modules of Finite Dimensional Hopf Algebras. In: Carlson, J., Iyengar, S., Pevtsova, J. (eds) Geometric and Topological Aspects of the Representation Theory of Finite Groups. PSSW 2016. Springer Proceedings in Mathematics & Statistics, vol 242. Springer, Cham. https://doi.org/10.1007/978-3-319-94033-5_20

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