A natural map from a quantized space onto its semiclassical limit

ABSTRACT

Let $\hat{\Gamma }$ be the natural map given in [11, Section 1]. Here, we construct a deformation B_q of a Poisson algebra B₁ and a prime ideal P of B_q such that $\hat{\Gamma }\left(P\right)$ is not a Poisson prime ideal of B₁.

KEYWORDS:

• Deformation
• quantization
• semiclassical limit
• poisson algebra

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B63
• 16S36

Acknowledgments

The author is supported by National Research Foundation of Korea, Grant 2012-007347 and thanks for the Korea Institute for Advanced Study for the warm hospitality during the preparation of this paper.