## Group-type subfactors and Hadamard matrices

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- by Richard D. Burstein PDF
- Trans. Amer. Math. Soc.
**367**(2015), 6783-6807 Request permission

## 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.## References

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## Additional Information

**Richard D. Burstein**- Affiliation: Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240
- MR Author ID: 896764
- Email: richard.d.burstein@vanderbilt.edu
- Received by editor(s): November 13, 2009
- Received by editor(s) in revised form: February 9, 2010
- Published electronically: June 11, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**367**(2015), 6783-6807 - MSC (2010): Primary 46L37
- DOI: https://doi.org/10.1090/tran/5314
- MathSciNet review: 3378814