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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:727018 |
| Date | January 2017 |
| Creators | Nolan, Brendan |
| Contributors | Launois, Stephane ; Pech, Clelia |
| Publisher | University of Kent |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://kar.kent.ac.uk/64634/ |
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