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

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.

Poisson–Lie sigma models on Drinfel’d double

Jan Vysoký, Ladislav Hlavatý (2012)

Archivum Mathematicum

Similarity:

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

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.

Universal enveloping algebras and quantization

Grabowski, Janusz

Similarity:

It is shown how the universal enveloping algebra of a Lie algebra L can be obtained as a formal deformation of the Kirillov-Souriau Poisson algebra C ∞ ( L * ) of smooth functions on the dual of L . This deformation process may be viewed as a “quantization” in the sense of and [Ann. Phys. 111, 61-110 (1978; Zbl 0377.53024) and ibid., 111-151 (1978; Zbl 0377.53025)]. The result presented is a somewhat more elaborate version of earlier findings by [Lett. Math. Phys. 7, 249-258 (1983; Zbl 0522.58019)]...