# Trivalent Categories

OASW01 - Structure of operator algebras: subfactors and fusion categories

If N < M is a 2-supertransitive subfactor, then the N-N bimodule M splits up as N \oplus X for some simple bimodule X. This bimodule X has sime nice properties, for example the multiplication map on M restricts to a map X \otimes X \rightarrow X. I’ll discuss work with Scott Morrison and Emily Peters where we classify what other ways you can have a bimodule with such a multiplication map which don’t come from a subfactor. The techniques are planar algebraic and involve the discharging argument used in the proof of the 4-color theorem.

This talk is part of the Isaac Newton Institute Seminar Series series.