Homomorphisms between bubble algebra modules

Jegan, Mahadevan (2013). Homomorphisms between bubble algebra modules. (Unpublished Doctoral thesis, City University London)

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Abstract

In this thesis, we study the representation theory of the bubble algebras. We focus on determining the homomorphisms between cell modules for these algebras.

We show that the bubble algebras are cellular, and form a tower of recollement. By decomposing Gram matrices we are able to determine homomorphisms in the one arc case. We determine a generating set for the algebra (and its cardinality), and use this with a hypercuboid approach to determine homomorphisms in the general case. We end with a conjectural alternative approach to the general case involving matrix methods.

Item Type: Thesis (Doctoral)
Additional Information: © Copyright by Mahadevan Jegan, 2013
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
City University London PhD theses
URI: http://openaccess.city.ac.uk/id/eprint/2380

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