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New realizations of Lie algebra kappa-deformed Euclidean space. (English) Zbl 1191.81138
Summary: 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 Poincaré algebra and with the corresponding deformed coalgebra is constructed in a unified way.

MSC:
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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