Homological properties of quantized coordinate rings of semisimple groups

Abstract

We prove that the generic quantized coordinate ring O q ( G ) is Auslander-regular, Cohen–Macaulay, and catenary for every connected semisimple Lie group G. This answers questions raised by Brown, Lenagan, and the first author. We also prove that under certain hypotheses concerning the existence of normal elements, a noetherian Hopf algebra is Auslander–Gorenstein and Cohen–Macaulay. This provides a new set of positive cases for a question of Brown and the first author.