English

Support varieties and representation type of small quantum groups

Representation Theory 2011-02-22 v2 Quantum Algebra

Abstract

In this paper we provide a wildness criterion for any finite dimensional Hopf algebra with finitely generated cohomology. This generalizes a result of Farnsteiner to not necessarily cocommutative Hopf algebras over ground fields of arbitrary characteristic. Our proof uses the theory of support varieties for modules, one of the crucial ingredients being a tensor product property for some special modules. As an application we prove a conjecture of Cibils stating that small quantum groups of rank at least two are wild.

Keywords

Cite

@article{arxiv.0910.1383,
  title  = {Support varieties and representation type of small quantum groups},
  author = {Joerg Feldvoss and Sarah Witherspoon},
  journal= {arXiv preprint arXiv:0910.1383},
  year   = {2011}
}

Comments

14 pages; minor revisions; to appear in Int. Math. Res. Not

R2 v1 2026-06-21T13:55:31.699Z