A finiteness result for commuting squares with large second relative commutant
Author:
Remus Nicoara
Journal:
Trans. Amer. Math. Soc. 364 (2012), 36853698
MSC (2010):
Primary 46L37
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 extremalitylike 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 379960612 – and – Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania
DOI:
http://dx.doi.org/10.1090/S000299472012055322
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.
