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Title: Generalizations of Artin and Coxeter monoids
Author: Ffitch, Edward Stefan
ISNI:       0000 0004 8498 0412
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2019
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics