# zbMATH — the first resource for mathematics

Primitive ideals of the coordinate ring of quantum symplectic space. (English) Zbl 0828.17011
The author classifies the primitive spectrum of the coordinate ring $$R:= {\mathcal O}_q ({\mathfrak {sp}} \mathbb{C}^{2n})$$ of quantum symplectic space when $$q$$ is not a root of unity. This coordinate ring turns out to be an iterated Ore extension over $$\mathbb{C}$$, so the theory of skew polynomial rings plays a major role in the classification. The author replaces the canonical set of generators of $$R$$ by a larger set $$P$$, defines a notion of admissible subset of $$P$$, and then uses admissible subsets to parametrize the primitive spectrum of $$R$$. Some features of enveloping algebras of solvable Lie algebras reappear in this setting; all prime ideals are completely prime, all primitive factor algebras have even Gelfand-Kirillov dimension, and there is an analogue of the Tauvel height formula. On the other hand, the center of $$R$$ reduces to $$\mathbb{C}$$.

##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 16S30 Universal enveloping algebras of Lie algebras
Full Text: