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arXiv · 0811.1265

Group-type subfactors and Hadamard matrices

Richard D. Burstein
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Abstract

A hyperfinite $II_1$ 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 $R^H \subset R \rtimes K$, where $H$ and $K$ are finite groups with outer actions on the hyperfinite $II_1$ 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 $H^3(H \ast K / Int R)$ associated with the action.

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Richard D. Burstein. 2008-11-08. Group-type subfactors and Hadamard matrices. https://arxiv.org/abs/0811.1265

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