Homological properties of quantized coordinate rings of semisimple groups

Details Homological properties of quantized coordinate rings of semisimple groups Homological properties of quantized coordinate rings of semisimple groups

2005-10-19

arxiv.org/abs/math/0510420v1

Mathematics

Quantum Algebra

Scientific paper

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.

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