Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
Full-text PDF Free Access

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.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 46L37

Retrieve articles in all journals with MSC (2010): 46L37

Additional Information

Richard D. Burstein
Affiliation: Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240
MR Author ID: 896764

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