Homomorphisms between bubble algebra modules

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.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

City University London

Year dc:date.issued

2013

Author dc:creator

• Jegan, Mahadevan

• QA Mathematics