Poisson Lie groups and their relations to quantum groups
Volume 34 / 1995
Banach Center Publications 34 (1995), 55-64
DOI: 10.4064/-34-1-55-64
Abstract
The notion of Poisson Lie group (sometimes called Poisson Drinfel'd group) was first introduced by Drinfel'd [1] and studied by Semenov-Tian-Shansky [7] to understand the Hamiltonian structure of the group of dressing transformations of a completely integrable system. The Poisson Lie groups play an important role in the mathematical theories of quantization and in nonlinear integrable equations. The aim of our lecture is to point out the naturality of this notion and to present basic facts about Poisson Lie groups together with some relations to the recent work on quantum groups.
