Group-type subfactors and Hadamard matrices

Burstein, Richard

doi:10.1090/tran/5314

Group-type subfactors and Hadamard matrices

Author: Richard D. Burstein
Journal: Trans. Amer. Math. Soc. 367 (2015), 6783-6807
MSC (2010): Primary 46L37
DOI: https://doi.org/10.1090/tran/5314
Published electronically: June 11, 2015
MathSciNet review: 3378814
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Abstract: A hyperfinite $\mathrm {II}_1$ 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 $\mathrm {II}_1$ 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 $H^3(H \ast K / \mathrm {Int} R)$ associated with the action.

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