Representation theory of algebras related to the partition algebra

Banjo, Elizabeth (2013). Representation theory of algebras related to the partition algebra. (Unpublished Doctoral thesis, City University London)

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Abstract

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.

Item Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Divisions: City University London PhD theses
School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/2360

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