On quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions

Understand

Quantum deformations of (anti-)de Sitter 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 Poincar\'e 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 \kappa-deformation for the (2+1) (A)dS algebras and quantum spacetimes is given.