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Title: A strong Dixmier-Moeglin equivalence for quantum Schubert cells and an open problem for quantum Plücker coordinates
Author: Nolan, Brendan
ISNI:       0000 0004 6423 1086
Awarding Body: University of Kent
Current Institution: University of Kent
Date of Award: 2017
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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.
Supervisor: Launois, Stephane ; Pech, Clelia Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Q Science