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 | References | Similar Articles | Additional Information
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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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
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