Identifier

etd-07102016-204601

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

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.

Date

2016

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Yakimov, Milen

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