A finiteness result for commuting squares with large second relative commutant

Author:
Remus Nicoara

Journal:
Trans. Amer. Math. Soc. **364** (2012), 3685-3698

MSC (2010):
Primary 46L37

DOI:
https://doi.org/10.1090/S0002-9947-2012-05532-2

Published electronically:
February 16, 2012

MathSciNet review:
2901230

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Abstract: We prove that there exist only finitely many commuting squares of finite dimensional -algebras of fixed dimension, satisfying a ``large second relative commutant'' condition. We show this by studying the local minima of , where are fixed subalgebras of some -algebra and is a unitary.

When applied to lattices arising from subfactors satisfying a certain extremality-like condition, our result yields Ocneanu's finiteness theorem for the standard invariants of such finite depth subfactors.

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Additional Information

**Remus Nicoara**

Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-0612 – and – Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania

DOI:
https://doi.org/10.1090/S0002-9947-2012-05532-2

Received by editor(s):
August 19, 2010

Received by editor(s) in revised form:
December 26, 2010

Published electronically:
February 16, 2012

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.