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Displaying similar documents to “Skein quantization of Poisson algebras of loops on surfaces”

Racks and orbits of dressing transformations

A. A. Balinsky (2000)

Commentationes Mathematicae Universitatis Carolinae

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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.

Poisson–Lie sigma models on Drinfel’d double

Jan Vysoký, Ladislav Hlavatý (2012)

Archivum Mathematicum

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Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras....

Linearization and star products

Veronique Chloup (2000)

Banach Center Publications

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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.