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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Elsevier
2017-03-01
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Series: | Physics Letters B |
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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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institution | Directory Open Access Journal |
issn | 0370-2693 1873-2445 |
language | English |
last_indexed | 2024-12-20T17:16:21Z |
publishDate | 2017-03-01 |
publisher | Elsevier |
record_format | Article |
series | Physics Letters B |
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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