Auslander-Reiten theory of Frobenius-Lusztig kernels. (Q2865923)

The main result of this paper asserts the following: If \(\mathfrak{g}\) is a finite dimensional simple complex Lie algebra which is not isomorphic to \(\mathfrak{sl}_2\), then the tree class of any non-periodic component of the Frobenius-Lusztig kernel associated to \(\mathfrak{g}\) is one of the three infinite Dynkin diagrams. Furthermore, in the case of the small quantum group, if, additionally, the component in question contains the restriction of a module for the infinite dimensional Lusztig form of the quantum group, then the component is of type \(\mathbb{Z}[A_{\infty}]\).NEWLINENEWLINEFrom the text of the corrigendum: Recently, J. Feldvoss and S. Witherspoon have discovered a flaw in their theory of support varieties (see their erratum [Preprint,2013, \url{arxiv:1308.4928}]). This requires adding the assumption ``(qt) The Hopf algebra under assertion is quasi-triangular'' when using certain results on the support varieties. The results on quantum groups in our paper stay correct but require different proofs which are explained in this corrigendum.