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arXiv · hep-th/0311007

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

Yun Li·Sicong Jing
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Abstract

The quantum Euclidean space R_{q}^{N} is a kind of noncommutative space which 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 R_{q}^{3}. Motivated by realization of R_{q}^{3} by differential operators in R^{3}, we give such realization for R_{q}^{5} and R_{q}^{7} cases and generalize our results to R_{q}^{N} (N odd) in this paper, that is, we show that the algebra of R_{q}^{N} can be realized by differential operators acting on C^{infinite} functions on undeformed space R^{N}.

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Yun Li, Sicong Jing. 2003-11-03. Realization of the N(odd)-dimensional Quantum Euclidean Space by Differential Operators. https://doi.org/10.1088/0253-6102%2F41%2F2%2F175

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