The group of automorphisms of the coordinate ring of quantum symplectic space
type: Item
instance of: scholarly article
title: The group of automorphisms of the coordinate ring of quantum symplectic space
zbMATH Open document ID: 1016.16033
published in: Beiträge zur Algebra und Geometrie
publication date: 2003-02-10T00:00:00Z
full work available at URL: https://eudml.org/doc/122759
full work available at URL: 24.html
review text: Let \(R\) be the coordinate ring of the quantum symplectic space. \textit{J. Gómez-Torrecillas, L. El Kaoutit} and \textit{L. Benyakoub} [Commun. Algebra 29, No. 7, 3179-3197 (2001; Zbl 0999.16001)] presented an explicit description of the prime spectrum of \(R\), and it can be computed from this description the set of height one prime ideals. Since \(R\) is a PBW algebra and every nonzero element has an exponent, the authors prove that the generators of the height one primes are eigenvectors for each automorphism of \(R\). The main theorem is derived from the previous statement, and it says that the group of automorphisms of \(R\) is isomorphic to an algebraic torus.
reviewed by: F. J. Lobillo
Mathematics Subject Classification ID: 16W35
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 16D25
zbMATH DE Number: 1866015
zbMATH Keywords: coordinate rings
zbMATH Keywords: quantum symplectic spaces
zbMATH Keywords: automorphism groups
zbMATH Keywords: height one prime ideals
author: José Gómez-Torrecillas
author: Laiachi El Kaoutit
MaRDI profile type: Publication
Recommended article: The representations of the coordinate ring of the quantum symplectic space
Recommended article: Symplectic structures on groups of automorphisms of symmetric spaces
Recommended article: Q5482630
Recommended article: \(\pi_1\) of symplectic automorphism groups and invertibles in quantum homology rings
Recommended article: Q4891435
Recommended article: On the structure of quantum automorphism groups
Recommended article: Q5433043
Recommended article: Q3699919
Recommended article: Q6164770
Recommended article: The group of Poisson automorphisms of the Poisson symplectic space
description: scientific article; zbMATH DE number 1866015