Primitive ideals of the coordinate ring of quantum symplectic space
type: Item
instance of: scholarly article
title: Primitive ideals of the coordinate ring of quantum symplectic space
zbMATH Open document ID: 0828.17011
author: Sei-Qwon Oh
published in: Journal of Algebra
publication date: 1995-08-29T00:00:00Z
review text: 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 \(\mathbb{C}\).
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16S30
zbMATH DE Number: 783875
zbMATH Keywords: quantum symplectic group
zbMATH Keywords: primitive spectrum
zbMATH Keywords: coordinate ring
zbMATH Keywords: quantum symplectic space
zbMATH Keywords: iterated Ore extension
zbMATH Keywords: admissible subsets
reviewed by: William M. McGovern
MaRDI profile type: Publication
full work available at URL: jabr.1995.1138
OpenAlex ID: W2092577472
DOI: 10.1006/JABR.1995.1138
description: scientific article; zbMATH DE number 783875