Algebra automorphisms of quantized enveloping algebras \(U_ q({\mathfrak g})\)
type: Item
instance of: scholarly article
title: Algebra automorphisms of quantized enveloping algebras \(U_ q({\mathfrak g})\)
zbMATH Open document ID: 0810.17011
author: Jianguo Zha
published in: Science in China. Series A
publication date: 1994-11-03T00:00:00Z
review text: The algebra automorphisms of the quantized enveloping algebras \(U_ q({\mathfrak g})\) are discussed, where \(q\) is generic. Let \(G\) be the group consisting of all deformed algebra automorphisms of \(U_ q({\mathfrak g})\) and \(N\) be its subgroup consisting of all elements which are deformations of the identity automorphisms of \(U({\mathfrak g})\), then \(G/N\) is generated by the following five deformed automorphisms: (i) the Cartan involution, (ii) diagonal automorphisms, (iii) graph automorphisms, (iv) an automorphism \(\delta : \delta(E_ i) = \varepsilon_ i E_ i\), \(\delta(F_ i) = F_ i\), and \(\delta(K_ i) = \varepsilon_ i K_ i\), where \(1 \leq i \leq n\), \(\varepsilon_ i = \pm 1\), (v) the action of the braid group generated by \(T_ i\), which is established by Lusztig.
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 682143
zbMATH Keywords: automorphisms
zbMATH Keywords: quantized enveloping algebras
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 682143