Erratum to "Support varieties and representation type of small quantum groups"

TL;DR

This paper corrects previous results on support varieties and representation types of small quantum groups, clarifying the conditions needed for certain theorems and extending applicability to various Hopf algebras.

Contribution

It identifies necessary additional hypotheses for existing theorems and discusses alternative approaches for non-quasitriangular Hopf algebras.

Findings

Corrected theorems require quasitriangularity

Support variety theory applies to specific Hopf algebras

Hochschild support varieties can be used when quasitriangularity is absent

Abstract

Some of the general results in the paper require an additional hypothesis, such as quasitriangularity. Applications to specific types of Hopf algebras are correct, as some of these are quasitriangular, and for those that are not, the Hochschild support variety theory may be applied instead.