Relationship Between Quantum and Poisson Structures of Odd Dimensional Euclidean Spaces |
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Authors: | Sei-Qwon Oh Mi-Yeon Park |
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Institution: | 1. Department of Mathematics , Chungnam National University , Daejeon, Korea sqoh@cnu.ac.kr;3. Department of Mathematics , Chungnam National University , Daejeon, Korea |
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Abstract: | It is shown that the prime and primitive spectra of the multiparameter quantized algebra of odd-dimensional euclidean spaces are homeomorphic to the Poisson prime and Poisson primitive spectra of the multiparameter Poisson algebra of odd-dimensional euclidean spaces in the case when the multiplicative subgroup of a base field generated by the parameters is torsion free. As a corollary, it is shown that the prime and primitive spectra of the multiparameter quantized algebra of odd-dimensional euclidean spaces are topological quotients of the prime and maximal spectra of the corresponding commutative polynomial ring. |
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Keywords: | Poisson algebra Quantized euclidean space Topological quotient |
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