Displaying similar documents to “From double Lie groups to quantum groups”

Introduction to quantum Lie algebras

Gustav Delius (1997)

Banach Center Publications

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Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras U h ( g ) . The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. The recent general results about quantum Lie algebras are introduced with the help of the explicit example of ( s l 2 ) h .

Applications of Lie systems in quantum mechanics and control theory

José F. Cariñena, Arturo Ramos (2003)

Banach Center Publications

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Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically,...

Problems in the theory of quantum groups

Shuzhou Wang (1997)

Banach Center Publications

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This is a collection of open problems in the theory of quantum groups. Emphasis is given to problems in the analytic aspects of the subject.

Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations

Angel Ballesteros, Mariano del Olmo (1997)

Banach Center Publications

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Contractions of Poisson-Lie groups are introduced by using Lie bialgebra contractions. As an application, contractions of SL(2,R) Poisson-Lie groups leading to (1+1) Poincaré and Heisenberg structures are analysed. It is shown how the method here introduced allows a systematic construction of the Poisson structures associated to non-coboundary Lie bialgebras. Finally, it is sketched how contractions are also implemented after quantization by using the Lie bialgebra approach. ...

Anyonic Groups

Shahn Majid (1992)

Recherche Coopérative sur Programme n°25

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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...