New realizations of Lie algebra kappa-deformed Euclidean space

Abstract

We study Lie algebra $κ$-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 $κ$-deformed noncommutative space of the Lie algebra type with undeformed Poincar{é} algebra and with the corresponding deformed coalgebra is constructed in a unified way.