Homological properties of quantized coordinate rings of semisimple groups

Abstract

We prove that the generic quantized coordinate ring ${\mathcal{O}}_q(G)$ 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.

References in corpus (1)

• Algebraic structure of multi-parameter quantum groups

Cited by in corpus (2)

• On the Hochschild (co)homology of Quantum Homogeneous Spaces
• Calabi-Yau property under monoidal Morita-Takeuchi equivalence