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New realizations of Lie algebra kappa-deformed Euclidean space

We study Lie algebra κ-deformed Euclidean space with undeformed rotation algebra SOa(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.

noncommutative space; kappa-deformed space; deformed Poincaré algebra

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