New realizations of Lie algebra kappa-deformed Euclidean space

TL;DR

This paper explores various realizations of the $$-deformed Euclidean space using Lie algebra methods, constructing star products and a unified framework for the noncommutative space with undeformed rotation and Poincare9 algebra.

Contribution

It introduces multiple realizations of $$-deformed Euclidean space and develops a unified approach to its star product and algebraic structure.

Findings

Multiple realizations of $$-deformed Euclidean space are constructed.

A star product corresponding to each realization is derived.

A unified framework for the noncommutative space with undeformed rotation and Poincare9 algebra is established.

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.