Properties of Polynomial Identity Quantized Weyl Algebras
type: CreativeWork
description: In this work on Polynomial Identity (PI) quantized Weyl algebras we begin with a brief survey of Poisson geometry and quantum cluster algebras, before using these as tools to classify the possible centers of such algebras in two different ways. In doing so we explicitly calculate the formulas of the discriminants of these algebras in terms of a general class of central polynomial subalgebras. From this we can classify all members of this family of algebras free over their centers while proving that their discriminants have the properties of effectiveness and local domination. Applying these results to the family of tensor products of PI quantized Weyl algebras we solve the automorphism and isomorphism problems.
abstract: In this work on Polynomial Identity (PI) quantized Weyl algebras we begin with a brief survey of Poisson geometry and quantum cluster algebras, before using these as tools to classify the possible centers of such algebras in two different ways. In doing so we explicitly calculate the formulas of the discriminants of these algebras in terms of a general class of central polynomial subalgebras. From this we can classify all members of this family of algebras free over their centers while proving that their discriminants have the properties of effectiveness and local domination. Applying these results to the family of tensor products of PI quantized Weyl algebras we solve the automorphism and isomorphism problems.
author: Levitt, Jesse S. F.
keywords: Rings and Algebras, Quantum Algebra, Symplectic Ge
date published: 2016-01-01T08:00:00Z
date modified: 2026-07-24T02:59:31Z
provider: Lousiana State University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Mathematics

PropertyValue
property ID: DOI
value: 10.31390/gradschool_dissertations.1509