An introduction to quantum groups (Q1908937)

Quantum groups are Hopf algebras, which are in general noncommutative and noncocommutative deformations of two types of classical Hopf algebras -- the algebra of (rational) functions on an algebraic matrix group, and the universal enveloping algebra of a Lie algebra. In this article, we give a general introduction to the first type, for the groups \(\text{GL} (n)\) and \(\text{SL} (n)\) over a field. In section 2, we review the classical point of view, emphasizing Hopf algebra ideas. In section 3, we discuss the quantum analogues of the objects discussed in section 2. This article is based on a talk given at the Chinese University of Hong Kong in June, 1994.