Automorphisms of Bipartite Graph planar Algebras and their subfactor planar algebras[HBNI MSc 7]

Abstract

The concept of a Bipartite Graph Planar Algebra (BGPA) corresponding to a uniformly locally finite bipartite graph with a uniformly bounded spin function as well as the automorphism group of this planar algebra, is studied in this thesis. This has its origins in [J2] and [B]. It is shown that this group is isomorphic to the semidirect product of two special types of subgroups which are easily computable from the bipartite graph. We are interested in those group actions whose fixed point subalgebras are Subfactor Planar Algebras (SPAs) because new SPAs will produce new subfactors. Finally it is shown that the SPA of a ‘diagonal subfactor without cocycle’ can be obtatined by this fixed point technique.