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Homological properties of quantized coordinate rings of semisimple groups
Author(s) -
Goodearl K. R.,
Zhang J. J.
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdl022
Subject(s) - mathematics , noetherian , pure mathematics , ring (chemistry) , catenary , algebra over a field , set (abstract data type) , geometry , computer science , chemistry , organic chemistry , programming language
We prove that the generic quantized coordinate ringO 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.