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

TL;DR

This paper constructs the Poisson analogue of the kappa-(A)dS quantum algebra in (3+1) dimensions using the quantum duality principle, explicitly including the cosmological constant and deriving deformed Casimir functions.

Contribution

It provides an explicit Poisson-Lie structure for the kappa-(A)dS algebra in (3+1) dimensions, incorporating the cosmological constant as a contraction parameter and sketching a twisted Drinfel'd double version.

Findings

Explicit Poisson-Lie structure for kappa-(A)dS algebra

Deformed Casimir functions derived

Limit to kappa-Poincaré algebra as b3b5  0

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-Poincar\'e algebra in the bicrossproduct basis. A twisted version with Drinfel'd double structure of this kappa-(A)dS deformation is sketched.