The group of automorphisms of the coordinate ring of quantum symplectic space
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.
scientific article; zbMATH DE number 1866015