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
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.