Singly Generated Planar Algebras and Subfactors

Abstract: Jones' pictorial description of the standard invariant of a subfactor as a so-called planar algebra together with Popa's abstract characterization of the standard invariant leads to a generators and relations approach to subfactors. In this approach one can manipulate symmetry operators naturally associated to the subfactor by using a powerful diagrammatic calculus.

We will explain some of the ideas that make the concept of a planar algebra an efficient tool in subfactor theory and report on some results obtained in collaboration with Vaughan Jones.