History and perspectives of quantum groups
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.
scientific article; zbMATH DE number 5151050