Varieties for modules of finite dimensional Hopf algebras

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.

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