Beginnings and First Examples

Abstract

The origins of the subject of quantum groups lie in mathematical physics, about which we will say nothing except that it is the source of the word ‘quantum’ in the subject. As in physics, much of the research into quantum groups is aimed at developing ‘quantum analogues of classical phenomena’, a catch phrase whose imprecision has been exploited to the full. Two decades of research in the area have produced many thousands of papers going in a wide variety of directions. We shall not attempt any overview of this landscape, but instead will focus on some algebraic portions of its terrain. n any quantization.