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