Quantum and Poisson structures of multi-parameter symplectic and Euclidean spaces

A class of Poisson algebras A n , Γ P , Q considered as a Poisson version of the multiparameter quantized coordinate rings K n , Γ P , Q of symplectic and Euclidean 2 n-spaces is constructed and Poisson structures of A n , Γ P , Q are described. In particular, it is proved that the prime Poisson and...

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Bibliographic Details
Published in:Journal of algebra 2008-06, Vol.319 (11), p.4485-4535
Main Author: Oh, Sei-Qwon
Format: Article
Language:English
Subjects:
Poisson algebra
Primitive ideal
Quantized symplectic algebra
Topological quotient map
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Summary:A class of Poisson algebras A n , Γ P , Q considered as a Poisson version of the multiparameter quantized coordinate rings K n , Γ P , Q of symplectic and Euclidean 2 n-spaces is constructed and Poisson structures of A n , Γ P , Q are described. In particular, it is proved that the prime Poisson and Poisson primitive spectra of A n , Γ P , Q are homeomorphic to the prime and primitive spectra of K n , Γ P , Q in the case when the multiplicative subgroup of k × generated by all parameters in K n , Γ P , Q is torsion free and, as a corollary, that the prime and primitive spectra of K n , Γ P , Q are topological quotients of the prime and maximal spectra of the corresponding commutative polynomial ring.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2008.03.010