New realizations of Lie algebra kappa-deformed Euclidean space

Abstract

We study Lie algebra $\kappa$-deformed Euclidean space with undeformed rotation algebra $SO_a(n)$ and commuting vectorlike derivatives. Infinitely many realizations in terms of commuting coordinates are constructed and a corresponding star product is found for each of them. The $\kappa$-deformed noncommutative space of the Lie algebra type with undeformed Poincar{\'e} algebra and with the corresponding deformed coalgebra is constructed in a unified way.Comment: 30 pages, Latex, accepted for publication in Eur.Phys.J.C, some typos correcte