Group-type subfactors and Hadamard matrices

Abstract

A hyperfinite $I{I}_1$ subfactor may be obtained from a symmetric commuting square via iteration of the basic construction. For certain commuting squares constructed from Hadamard matrices, we describe this subfactor as a group-type inclusion $R^H\subset R⋊K$, where $H$ and $K$ are finite groups with outer actions on the hyperfinite $I{I}_1$ factor $R$. We find the group of outer automorphisms generated by $H$ and $K$, and use the method of Bisch and Haagerup to determine the principal and dual principal graphs. In some cases a complete classification is obtained by examining the element of $H^3(H\ast K/IntR)$ associated with the action.

51 pages

References in corpus (1)

• Subfactors and Hadamard Matrices