History and perspectives of quantum groups
type: Item
instance of: scholarly article
title: History and perspectives of quantum groups
zbMATH Open document ID: 1117.17004
published in: Milan Journal of Mathematics
publication date: 2007-05-09T00:00:00Z
review text: This is as historical account on quantum group theory written by one of its inventors. The author begins with the theory of quantum spin chain, the search for an algebraic description of the Lax operators led to the first example of deformation of the universal enveloping algebra, \(U_q(\text{su}(2))\). In the next section the author explains the Yang-Baxter relation, firstly imposed by him and Takhtajan, as the condition for the unambiguity of the reduction of a monomial in possibly many ways. Then he recalls the role of Drinfeld, who introduced the notion of universal \(R\)-matrix and of course the name ``quantum group'' itself. The last section discusses some applications of quantum groups such as knot invariant and conformal field theory.
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 17-03
Mathematics Subject Classification ID: 20G42
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 5151050
author: L. D. Faddeev
MaRDI profile type: Publication
full work available at URL: s00032-006-0062-4
OpenAlex ID: W2003689050
DOI: 10.1007/S00032-006-0062-4
description: scientific article; zbMATH DE number 5151050