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

Abstract

The quantum duality principle is used to obtain explicitly the Poisson analogue of the kappa-(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 $\Lambda$ is included as a Poisson-Lie group contraction parameter, and the limit $\Lambda \to 0$ leads to the well-known kappa-Poincaré algebra in the bicrossproduct basis. A twisted version with Drinfel'd double structure of this kappa-(A)dS deformation is sketched.

13 pages

References in corpus (6)

• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
• Canonical and Lie-algebraic twist deformations of $\kappa$-Poincare and contractions to $\kappa$-Galilei algebras
• (Anti)de Sitter/Poincare symmetries and representations from Poincare/Galilei through a classical deformation approach

Cited by in corpus (6)

• The $\kappa$-(A)dS noncommutative spacetime
• Noncommutative spaces of worldlines
• Curved momentum spaces from quantum groups with cosmological constant
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• $\kappa$-de Sitter and $\kappa$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant
• The noncommutative space of light-like worldlines