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Title: Polycyclic monoids and their generalisations
Author: Jones, David G.
ISNI:       0000 0004 2712 1056
Awarding Body: Heriot-Watt University
Current Institution: Heriot-Watt University
Date of Award: 2011
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This thesis can be split into two parts. The first was inspired by a monograph by Bratteli and Jorgensen. We study arbitrary, not necessarily transitive, strong actions of polycyclic inverse monoids Pn. We obtain some new results concerning the strong actions of P2 on Z determined by the choice of one positive odd number p. We show that the structure of the representation can be explained by studying the binary representations of the numbers 1/p, 2/p,..., p−1/p . We also generalise the connection between the positively self conjugate submonoids of Pn and congruences on the free monoid A∗/n developed by Meakin and Sapir. The second part can be seen as a generalisation of the first. Graph inverse semigroups generalise the polycyclic inverse monoids and play an important role in the theory of C∗-algebras. We provide an abstract characterisation of graph inverse semigroups and show how they may be completed to form what we call the Cuntz-Krieger semigroup of the graph — this semigroup is then the semigroup analogue of the Leavitt path algebra of the graph. We again generalise the connection of Meakin and Sapir this time to certain subsemigroups of the graph inverse semigroup and congruences on the free graph.
Supervisor: Lawson, Mark V. Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available