Subfactor

Summary

A subfactor is an inclusion $N \subseteq M$ of factors, von Neumann algebras with trivial center, that share the same identity. For factors of type $\mathrm{II}_1$, Vaughan Jones attached to such an inclusion a number $[M:N]$, the index. It measures the relative size of $M$ over $N$. The Jones index theorem shows that the possible index values are surprisingly restricted. Subfactor theory connects operator algebras with knot invariants, quantum groups, tensor categories and conformal field theory.