The κ-(A)dS quantum algebra in (3+1) dimensions

The quantum duality principle is used to obtain explicitly the Poisson analogue of the κ-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson–Lie structure on the dual solvable Lie group. The construction is fully performed in a kinematical basis and deformed Casimir functions are...

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Main Authors: Ángel Ballesteros, Francisco J. Herranz, Fabio Musso, Pedro Naranjo
Format: Article
Language:English
Published: Elsevier 2017-03-01
Series:Physics Letters B
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S0370269317300278
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author Ángel Ballesteros
Francisco J. Herranz
Fabio Musso
Pedro Naranjo
author_facet Ángel Ballesteros
Francisco J. Herranz
Fabio Musso
Pedro Naranjo
author_sort Ángel Ballesteros
collection DOAJ
description The quantum duality principle is used to obtain explicitly the Poisson analogue of the κ-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson–Lie structure on the dual solvable Lie group. The construction is fully performed in a kinematical basis and deformed Casimir functions are also explicitly obtained. The cosmological constant Λ is included as a Poisson–Lie group contraction parameter, and the limit Λ→0 leads to the well-known κ-Poincaré algebra in the bicrossproduct basis. A twisted version with Drinfel'd double structure of this κ-(A)dS deformation is sketched.
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spelling doaj.art-489e1827d1b54812814a1e350fd8d6172022-12-21T19:31:59ZengElsevierPhysics Letters B0370-26931873-24452017-03-01766C20521110.1016/j.physletb.2017.01.020The κ-(A)dS quantum algebra in (3+1) dimensionsÁngel Ballesteros0Francisco J. Herranz1Fabio Musso2Pedro Naranjo3Departamento de Física, Universidad de Burgos, E-09001 Burgos, SpainDepartamento de Física, Universidad de Burgos, E-09001 Burgos, SpainIstituto Comprensivo “Leonardo da Vinci”, Via della Grande Muraglia 37, I-0014 Rome, ItalyDepartamento de Física, Universidad de Burgos, E-09001 Burgos, SpainThe quantum duality principle is used to obtain explicitly the Poisson analogue of the κ-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson–Lie structure on the dual solvable Lie group. The construction is fully performed in a kinematical basis and deformed Casimir functions are also explicitly obtained. The cosmological constant Λ is included as a Poisson–Lie group contraction parameter, and the limit Λ→0 leads to the well-known κ-Poincaré algebra in the bicrossproduct basis. A twisted version with Drinfel'd double structure of this κ-(A)dS deformation is sketched.http://www.sciencedirect.com/science/article/pii/S0370269317300278Anti-de SitterCosmological constantQuantum groupsPoisson–Lie groupsLie bialgebrasQuantum duality principle
spellingShingle Ángel Ballesteros
Francisco J. Herranz
Fabio Musso
Pedro Naranjo
The κ-(A)dS quantum algebra in (3+1) dimensions
Physics Letters B
Anti-de Sitter
Cosmological constant
Quantum groups
Poisson–Lie groups
Lie bialgebras
Quantum duality principle
title The κ-(A)dS quantum algebra in (3+1) dimensions
title_full The κ-(A)dS quantum algebra in (3+1) dimensions
title_fullStr The κ-(A)dS quantum algebra in (3+1) dimensions
title_full_unstemmed The κ-(A)dS quantum algebra in (3+1) dimensions
title_short The κ-(A)dS quantum algebra in (3+1) dimensions
title_sort κ a ds quantum algebra in 3 1 dimensions
topic Anti-de Sitter
Cosmological constant
Quantum groups
Poisson–Lie groups
Lie bialgebras
Quantum duality principle
url http://www.sciencedirect.com/science/article/pii/S0370269317300278
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