Primitive ideals of \({\mathbf C}_ q[SL(3)]\)
type: Item
instance of: scholarly article
title: Primitive ideals of \({\mathbf C}_ q[SL(3)]\)
zbMATH Open document ID: 0801.17012
DOI: 10.1007/BF02096864
author: Timothy J. Hodges
author: Thierry Levasseur
published in: Communications in Mathematical Physics
publication date: 1994-11-30T00:00:00Z
review text: The authors' summary: The primitive ideals of the Hopf algebra \(C_ q [SL(3)]\) are classified. In particular, it is shown that the orbits in Prim \(C_ q [SL(3)]\) under the action of the representation group \(H \cong C^* \times C^*\) are parameterized naturally by \(W \times W\), where \(W\) is the associated Weyl group. It is shown that there is a natural one-to-one correspondence between primitive ideals of \(C_ q [SL(3)]\) and symplectic leaves of the associated Poisson algebraic group \(SL(3,\mathbb{C})\).
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 487163
zbMATH Keywords: quantum group
zbMATH Keywords: Poisson Lie group
zbMATH Keywords: primitive ideals
zbMATH Keywords: Hopf algebra
zbMATH Keywords: symplectic leaves
reviewed by: Fang Li
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 487163