Braided identities, quantum groups, and Clifford algebras
type: Item
instance of: scholarly article
title: Braided identities, quantum groups, and Clifford algebras
zbMATH Open document ID: 0976.17008
DOI: 10.1023/A:1003770924549
author: César Bautista
published in: International Journal of Theoretical Physics
publication date: 2001-06-10T00:00:00Z
review text: For the Lie algebra \({\mathfrak g}=sl^+_{n+1}\) (upper triangular matrices), the author constructs a deformation (quantum Lie algebra \({\mathfrak g}_q)\) and a generalized universal enveloping algebra \(U({\mathfrak g}_q)\) such that \(U({\mathfrak g}_q) =U_q({\mathfrak g})\), the quantum group of \({\mathfrak g}\), and such that \({\mathfrak g}_q\to {\mathfrak g}\) and \(U({\mathfrak g}_q) \to U({\mathfrak g})\) as \(q \to 1\). \({\mathfrak g}_q\) is a Lie algebra in a braided category and \(U({\mathfrak g}_q)\) is a braided Hopf algebra. Relations to Clifford algebras are discussed.
reviewed by: Earl J. Taft
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 18E10
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 1602929
zbMATH Keywords: quantum Lie algebra
zbMATH Keywords: generalized universal enveloping algebra
zbMATH Keywords: quantum group
zbMATH Keywords: braided category
zbMATH Keywords: braided Hopf algebra
zbMATH Keywords: Clifford algebras
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1602929