Displaying similar documents to “Preface, Contents”

Deformation on phase space.

Oscar Arratia, M.ª Angeles Martín Mínguez, María Angeles del Olmo (2002)

RACSAM

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El trabajo que presentamos constituye una revisión de varios procedimientos de cuantización basados en un espacio de fases clásico M. Estos métodos consideran a la mecánica cuántica como una "deformación" de la mecánica clásica por medio de la "transformación" del álgebra conmutativa C(M) en una nueva álgebra no conmutativa C(M). Todas estas ideas conducen de modo natural a los grupos cuánticos como deformación (o cuantización en un sentido amplio) de los grupos de Poisson-Lie, lo cual...

Poisson boundaries of discrete quantum groups

Reiji Tomatsu (2010)

Banach Center Publications

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This is a survey article about a theory of a Poisson boundary associated with a discrete quantum group. The main problem of the theory, that is, the identification problem is explained and solved for some examples.

A characterization of coboundary Poisson Lie groups and Hopf algebras

Stanisław Zakrzewski (1997)

Banach Center Publications

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We show that a Poisson Lie group (G,π) is coboundary if and only if the natural action of G×G on M=G is a Poisson action for an appropriate Poisson structure on M (the structure turns out to be the well known π + ). We analyze the same condition in the context of Hopf algebras. A quantum analogue of the π + structure on SU(N) is described in terms of generators and relations as an example.

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.