Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.752579
Title: One-parameter groups of Möbius maps in two-dimensional real commutative algebra
Author: Mustafa, Khawlah Ali
ISNI:       0000 0004 7425 7095
Awarding Body: University of Leeds
Current Institution: University of Leeds
Date of Award: 2018
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Abstract:
Möbius transformations have been thoughtfully studied over the field of complex numbers. In this thesis, we investigate Möbius transformations over two rings which are not fields: the ring of double numbers $\mathbb O$ and the ring of dual numbers $\mathbb D$. We will see certain similarity between the cases of fields and rings along with some significant distinctions. After the introduction and necessary background material, given in the first two chapters, I introduce general linear groups, projective lines and Möbius transformations over several rings such us the ring of integer numbers, the Cartesian product ring and the two rings $\mathbb O$ and $\mathbb D.$ In the following chapters, we consider in details metrics, classification of Möbius maps based on the number of fixed points, connected continuous one-parameter subgroups and an application of Möbius maps.
Supervisor: Kisil, Vladimir Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.752579  DOI: Not available
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