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Group-type subfactors and Hadamard matrices

Author: Richard D. Burstein
Journal: Trans. Amer. Math. Soc. 367 (2015), 6783-6807
MSC (2010): Primary 46L37
Published electronically: June 11, 2015
MathSciNet review: 3378814
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Abstract: A hyperfinite $ \textup {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 $ \textup {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 / \textup {Int} R)$ associated with the action.

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Additional Information

Richard D. Burstein
Affiliation: Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240

Keywords: Subfactor, commuting square, Hadamard matrix, automorphism
Received by editor(s): November 13, 2009
Received by editor(s) in revised form: February 9, 2010
Published electronically: June 11, 2015
Article copyright: © Copyright 2015 American Mathematical Society