Properties of Polynomial Identity Quantized Weyl Algebras

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.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2016

Author dc:creator

• Levitt, Jesse S. F.

• Rings and Algebras
• Quantum Algebra
• Symplectic Ge

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-07102016-204601
https://repository.lsu.edu/gradschool_dissertations/1509

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-2508