Quantum deformation of classical groups
Let \(A(G)\) be the coordinate algebra of a Lie group \(G\). A quantum deformation \(A(G_ q)\) of \(A(G)\) is a one-parameter family of Hopf algebras whose representation theories are the same as those of \(A(G)\). The author constructs the quantum deformations of \(A(O(N))\), \(A(SO(N))\) and \(A(Sp(N))\) by using Jimbo's solutions of the Yang-Baxter equation and determines their Peter-Weyl decompositions. For this purpose, he investigates the so-called quantum matrix bialgebras, and defines Hopf algebras \(A(G_ q)\) as quotients of corresponding quantum matrix bialgebras. Also, he studies group-like elements of these quantum matrix bialgebras and gives a new realization of the universal \(R\)-matrix.
scientific article; zbMATH DE number 548922