Preface, Contents
(1997)
Banach Center Publications
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Displaying similar documents to “Introduction to quantum Lie algebras”
Preface, Contents
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.
Quantum dynamics on the worldvolume from classical cohomology.
Isidro, José M., Fernández de Córdoba, Pedro (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Quantum integrable systems
Michael Semenov-Tian-Shansky (1993-1994)
Séminaire Bourbaki
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Quantum probability, renormalization and infinite-dimensional *-Lie algebras.
Accardi, Luigi, Boukas, Andreas (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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The catenarity of the positive part of the quantized enveloping algebra of a simple Lie algebra of type . (La caténarité de la partie positive de l'algèbre enveloppante quantifiée de l'algèbre de Lie simple de type .)
Malliavin, Marie Paule (1994)
Beiträge zur Algebra und Geometrie
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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,...
Quantum spaces: notes and comments on a lecture by S. L. Woronowicz
R. Budzyński, W. Kondracki (1995)
Banach Center Publications
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Deformed commutators on comodule algebras over coquasitriangular Hopf algebras
Zhongwei Wang, Guoyin Zhang, Liangyun Zhang (2015)
Colloquium Mathematicae
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We construct quantum commutators on comodule algebras over coquasitriangular Hopf algebras, so that they are quantum group coinvariant and have the generalized antisymmetry and Leibniz properties. If the coquasitriangular Hopf algebra is additionally cotriangular, then the quantum commutators satisfy a generalized Jacobi identity, and turn the comodule algebra into a quantum Lie algebra. Moreover, we investigate the projective and injective dimensions of some Doi-Hopf modules over a...
Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator
Eugen Paal, Jüri Virkepu (2011)
Banach Center Publications
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Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional real Lie algebras. The Jacobi operators of these quantum algebras are explicitly calculated.
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. ...
Braided modules and reflection equations
Dimitri Gurevich (1997)
Banach Center Publications
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We introduce a representation theory of q-Lie algebras defined earlier in [DG1], [DG2], formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in particular, those based on the so-called reflection equations. We also investigate the truncated tensor product of braided modules.