Relationship Between Quantum and Poisson Structures of Odd Dimensional Euclidean Spaces

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.

Key Words:

• Poisson algebra
• Quantized euclidean space
• Topological quotient

2000 Mathematics Subject Classification:

• 17B63
• 16W35

ACKNOWLEDGMENT

This work is supported by the Korea Research Foundation Grant, KRF-2007-314-C00007.

Notes

Communicated by T. Lenagan.