From “Quantum Groups” to “Quasi-Quantum Groups”

Abstract

The purpose of this lecture is not to review once more the theory of quantum groups, but to give a brief introduction to the recent work of Drinfeld1, where he presented a new (quantum) object, the quasi-Hopf algebras, which leads to generalizations of quantum groups that, to my knowledge, had not yet been proposed, and, in an even shorter summary, the definition and properties of the Lie quasi-bialgebras 1 and quasi-Poisson Lie groups 2, which constitute the classical limit of Drinfeld’s quantum objects.