Elementary Introduction to Quantum Groups

Abstract

This paper is an excellent introductory survey on quantumgroups. The topics are motivated by the theory of classicalintegral systems and the problem of their quantization. The basicconcepts of Poisson manifolds, Hopf algebras and Poisson Liegroups are carefully introduced. The classical and quantum YangBaxter equations are set up in connection with the Liouvillemodel on a lattice. Quantum matrix algebras, quantum groups andquantum vector spaces are defined following the lines of the wellknown paper of N. Yu. Reshetikhin, L. A. Takhtajan and L. D.Faddeev [Algebra i Analiz 1 (1989), no. 1, 178 206; MR\Cite{Reshetikhin89:Quantization:178--206}[90j:17039]]. Someelementary examples are given. A complete bibliography ends thepaper.\par {For the entire collection see MR 95a:58002.}