2013/02/28 by Ángel Ballesteros, Angel Ballesteros, Francisco J. Herranz +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Anti-de Sitter space #Black Holes and Theoretical Physics #Cosmological constant #De Sitter universe #Generalization #Isotropy #Lie algebra #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Quantum #Quantum mechanics #Space (punctuation) #Universe #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1742-6596/532/1/012002
published as J. Phys.: Conf. Ser. 532 (2014) 012002 · 15 pages, contribution presented at the Conference "3Quantum: Algebra, Geometry, Information", Tallinn (Estonia), July 2012. Minor corrections, one reference added
arxiv created 2013/08/04 · openalex publication_date 2014/09/10 · arxiv updated 2014/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum deformations of (anti-)de Sitter (A)dS algebras in (2+1) dimensions are revisited, and several features of these quantum structures are reviewed. In particular, the classification problem of (2+1) (A)dS Lie bialgebras is presented and the associated noncommutative quantum (A)dS spaces are also analysed. Moreover, the flat limit (or vanishing cosmological constant) of all these structures leading to (2+1) quantum Poincare algebras and groups is simultaneously given by considering the cosmological constant as an explicit Lie algebra parameter in the (A)dS algebras. By making use of this classification, a three-parameter generalization of the K-deformation for the (2+1) (A)dS algebras and quantum spacetimes is given. Finally, the same problem is studied in (3+1) dimensions, where a two-parameter generalization of the κ-(A)dS deformation that preserves the space isotropy is found.