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

Abstract

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.

Keywords

• Anti-de Sitter
• Cosmological constant
• Quantum groups
• Poisson–Lie groups
• Lie bialgebras
• Quantum duality principle