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Generalizations of Artin and Coxeter monoids
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Ffitch, Edward Stefan (2019) Generalizations of Artin and Coxeter monoids. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3423507~S15
Abstract
This thesis is divided into three chapters.
The first chapter looks at a class of generalized Coxeter monoids, the 'CI-monoids' appearing in [23]. We extend results by S.V. Tsaranov [28] and classify all the CI-monoids that have a zero element - an element of the monoid absorbing anything on the left and right. Following this, we partially resolve the classification of the finite CI-monoids, making use of the theory of rewriting systems [20].
The second chapter is an investigation into a related class of monoids, the 'AI-monoids' appearing in [23]. In accordance with [9, 12], we conjecture that every AI-monoid A has a finite Garside family, a distinguished subfamily of A such that every element of A has a certain 'greedy' normal decomposition. We establish the conjecture for a number of cases, and resolve Conjecture 11.12 of [23].
The final chapter extends partial results to the Embedding Conjecture for the monoid of left self-distributivity MLD, as presented by P. Dehornoy [4, p. 428-436, §9.6], [5, p. 518-524, §11.3]. After outlining the theory of leftdistributivity, we consider orthogonality properties of MLD and use these to establish the Embedding Conjecture for other large subfamilies of MLD not previously considered.
| Item Type: | Thesis or Dissertation (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Monoids -- Research, Coxeter groups, Artin's conjecture | ||||
| Official Date: | February 2019 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Krammer, Daan | ||||
| Extent: | ix, 164 leaves | ||||
| Language: | eng |
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