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19th Annual Great Plains Operator Theory Symposium
May 26-30, 1999
Iowa State University
Ames, IA, USA |
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Organizers
Justin Peters, Yiu Tung Poon, Bruce Wagner
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The Indecomposability of Free Group Factors over Nonprime Subfactors and Abelian Subalgebras
by
Marius B. Stefan
University of Iowa
We use Voiculescu's free entropy to show that the free group factors L(Fn)
cannot be decomposed as
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sp
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||·||2
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å
[(1 <= j1, ... , jt+1 <= f) || (1 <= t <= d)]
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Nj1ZNj2Z ... NjtZNjt+1 |
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or as
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sp
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||·||2
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å
[(1 <= j1, ... , jt+1 <= f) || (1 <= t <= d)]
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Aj1ZAj2Z ... AjtZAjt+1 |
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if N1, ... , Nf are
nonprime subfactors, A1, ... , Af are abelian *-subalgebras, Z is a
subset of L(Fn) containing p self-adjoint elements, and n >= p+2f+2.
In particular, it follows that L(Fn) =/= [`sp] R1R2 ... Rf and L(Fn) =/= [`sp] A1A2 ... Af if
R1, ... , Rf are hyperfinite subalgebras of L(Fn),
A1, ... , Af are abelian *-subalgebras of L(Fn), and n >= 2f+3,
thus settling a conjecture of L. Ge and S. Popa (for n=\infty).
Date received: April 12, 1999
Copyright © 1999 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cacw-24.