Realization of the N（odd）-Dimensional Quantum Euclidean Space by Differential Operators

The quantum Euclidean space Rq^N is a kind of noncommutative space that is obtained from ordinary Euclidean space R^N by deformation with parameter q. When N is odd, the structure of this space is similar to Rq^3.Motivated by realization of Rq^3 by differential operators in Rq^3, we give such realization for Rq^5 and Rq^7 cases and generalizeour results to Rq^N (N odd) in this paper, that is, we show that the algebra of Rq^N can be realized by differential operators acting on C^∞ functions on undeformed space R^N.

The quantum Euclidean space is a kind of noncommutative space that is obtained from ordinary Euclidean space by deformation with parameter q. When N is odd, the structure of this space is similar to . Motivated by realization of by differential operators in , we give such realization for and cases and generalize our results to (N odd) in this paper, that is, we show that the algebra of can be realized by differential operators acting on C∞ functions on undeformed space .