Displaying similar documents to “Applications of Lie systems in quantum mechanics and control theory”

From double Lie groups to quantum groups

Piotr Stachura (2005)

Fundamenta Mathematicae

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It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.

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 .

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. ...

Lie systems: theory, generalisations, and applications

J. F. Cariñena, J. de Lucas

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Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule. Apart from this fundamental property, Lie systems enjoy many other geometrical features and they appear in multiple branches of mathematics and physics. These facts, together with the authors' recent findings...