Eur. Phys. J. C (2006) 47: 531-539
https://doi.org/10.1140/epjc/s2006-02584-8

Theoretical Physics

New realizations of Lie algebra kappa-deformed Euclidean space

Rudjer Bošković Institute, Bijenička c. 54, 10002, Zagreb, Croatia

^* e-mail: meljanac@thphys.irb.hr

Received: 3 February 2006
Revised: 10 April 2006
Published online: 27 June 2006

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 Poincaré algebra and with the corresponding deformed coalgebra is constructed in a unified way.