On Hopf algebra deformation approach to renormalization.

Ionescu, Lucian M.; Marsalli, Michael

Displaying similar documents to “On Hopf algebra deformation approach to renormalization.”

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. ...

Quantum dynamics on the worldvolume from classical $s u (n)$ cohomology.

Isidro, José M., Fernández de Córdoba, Pedro (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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$κ$ -Minkowski spacetimes and DSR algebras: fresh look and old problems.

Borowiec, Andrzej, Pachol, Anna (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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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 ${(s l_{2})}_{h}$ .

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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Twist quantization of string and Hopf algebraic symmetry.

Asakawa, Tsuguhiko, Watamura, Satoshi (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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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.

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...

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.