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Title: Type III subfactors and planar algebras
Author: Shelly, Claire
ISNI:       0000 0004 2735 5071
Awarding Body: Cardiff University
Current Institution: Cardiff University
Date of Award: 2012
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In this thesis we investigate the theory of planar algebras for type III subfactors. We show directly how to associate a planar algebra to a type III subfactor using endomorphisms and intertwiners. We begin by describing how to define a type III version of the Temperley-Lieb planar algebra before giving a general definition of a type III planar algebra. We define a presenting map using endomorphisms and intertwiners and prove that this defines a type III subfactor planar algebra. We show that the definition of a type III subfactor planar algebra may be extended by removing the sphericality condition. We also investigate the reverse implication, and show that if we start with a type III subfactor planar algebra we can produce a type III subfactor using techniques from Guionnet-Jones-Shlyakhtenko and free probability. In the final chapter we investigate the type III version of A2 planar algebras. We extend the results of Chapter 3 to the A2 setting, defining a type III string algebra for SU(3) ADE graphs and relating this to planar algebras. We also discuss further work here relating to A2 planar algebras.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics