Poisson structures of multi-parameter symplectic and Euclidean spaces

2003/08/06 by Sei‐Qwon Oh, Sei-Qwon Oh, Oh, Sei-Qwon
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.QA #msc:17B63

paper · pdf · doi:10.48550/arxiv.math/0308047

31 pages

arxiv created 2003/08/06 · arxiv updated 2009/12/01

Abstract

A class of Poisson algebras considered as a Poisson version of the multiparameter quantized coordinate rings of symplectic and Euclidean 2n-spaces is constructed and the prime Poisson ideals and the symplectic ideals of these Poisson algebras are described. As a result, it is shown that the multiparameter quantized symplectic and Euclidean 2n-spaces are topological quotients of their classical spaces.

Related

• Double Poisson algebras
• The prime and primitive spectra of multiparameter quantum symplectic and euclidean spaces
• Poisson Hopf algebras associated to quantized enveloping algebras
• Towards Homotopy Poisson-n Algebras from N-plectic Structures
• Poisson cohomology and quantization