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A strong Dixmier-Moeglin equivalence for quantum Schubert cells and an open problem for quantum Plücker coordinates

Nolan, Brendan (2017) A strong Dixmier-Moeglin equivalence for quantum Schubert cells and an open problem for quantum Plücker coordinates. Doctor of Philosophy (PhD) thesis, University of Kent,. (KAR id:64634)

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Abstract

In this thesis, the algebras of primary interest are the quantum Schubert cells and the quantum Grassmannians, both of which are known to satisfy a condition on primitive ideals known as the Dixmier-Moeglin equivalence.

A stronger version of the Dixmier-Moeglin equivalence is introduced - a version which deals with all prime ideals of an algebra rather than just the primitive ideals. Quantum Schubert cells are shown to satisfy the strong Dixmier-Moeglin equivalence.

Until now, given a torus-invariant prime ideal of the quantum Grassmannian, one

could not decide which quantum Plücker coordinates it contains. Presented here is a graph-theoretic method for answering this question. This may be useful for providing a full description of the inclusions between the torus-invariant prime ideals of the quantum Grassmannian and may lead to a proof that quantum Grassmannians satisfy the strong Dixmier-Moeglin equivalence.

Item Type: Thesis (Doctor of Philosophy (PhD))
Thesis advisor: Launois, Stephane
Thesis advisor: Pech, Clelia
Uncontrolled keywords: Noncommutative algebra, quantum algebra, quantum groups, representation theory, Goodearl-Letzter H-stratification.
Subjects: Q Science
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
SWORD Depositor: System Moodle
Depositing User: System Moodle
Date Deposited: 22 Nov 2017 17:13 UTC
Last Modified: 11 Dec 2022 16:19 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/64634 (The current URI for this page, for reference purposes)

University of Kent Author Information

Nolan, Brendan.

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