2003/12/18 by Piotr Kosiński, Kosiński, P., J. Lukierski +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.hep-th/0312227
openalex publication_date 2003/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is presented on the occasion of 60-th birthday of Jose Adolfo de Azcarraga who in his very rich scientific curriculum vitae has also a chapter devoted to studies of quantum-deformed symmetries, in particular deformations of relativistic and Galilean space-time symmetries [1-4]. In this paper we provide new steps toward describing the κ-deformed D=4 conformal group transformations. We consider the quantization of D=4 conformal group with dimensionful deformation parameter κ. Firstly we discuss the noncommutativity following from the Lie-Poisson structure described by the light-cone κ-Poincaré r-matrix. We present complete set of D=4 conformal Lie-Poisson brackets and discuss their quantization. Further we define the light-cone κ-Poincaré quantum R-matrix in O(4,2) vector representation and discuss the inclusion of noncommutative conformal translations into the framework of κ-deformed conformal quantum group. The problem with real structure of κ-deformed conformal group is pointed out.