Displaying similar documents to “A characterization of coboundary Poisson Lie groups and Hopf algebras”

Poisson Lie groups and their relations to quantum groups

Janusz Grabowski (1995)

Banach Center Publications

Similarity:

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...

Quantization of pencils with a gl-type Poisson center and braided geometry

Dimitri Gurevich, Pavel Saponov (2011)

Banach Center Publications

Similarity:

We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson...

Racks and orbits of dressing transformations

A. A. Balinsky (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A new algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This gives the topological interpretation of the link invariants associated with the Weinstein-Xu classical solutions of the quantum Yang-Baxter equation. Some applications to the three-dimensional topological quantum field theories are discussed.

Linearization and star products

Veronique Chloup (2000)

Banach Center Publications

Similarity:

The aim of this paper is to give an overview concerning the problem of linearization of Poisson structures, more precisely we give results concerning Poisson-Lie groups and we apply those cohomological techniques to star products.