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Title: Representation theory of algebras related to the partition algebra
Author: Banjo, Elizabeth
ISNI:       0000 0004 2735 401X
Awarding Body: City University
Current Institution: City, University of London
Date of Award: 2013
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The main objective of this thesis is to determine the complex generic representation theory of the Juyumaya algebra. We do this by showing that a certain specialization of this algebra is isomorphic to the small ramified partition algebra, introduced by Martin (the representation theory of which is computable by a combination of classical and category theoretic techniques). We then use this result and general arguments of Cline, Parshall and Scott to prove that the Juyumaya algebra En(x) over the complex field is generically semisimple for all n 2 N. The theoretical background which will facilitate an understanding of the construction process is developed in suitable detail. We also review a result of Martin on the representation theory of the small ramified partition algebra, and fill in some gaps in the proof of this result by providing proofs to results leading to it.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics