Journal of Operator Theory

Volume 44, Issue 2, Fall 2000 pp. 335-345.

Cohomology for finite index inclusions of factors

Authors: Allan M. Sinclair (1), and Roger R. Smith (2)
Author institution: (1) Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland
(2) Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

Summary: If

$\caln \subseteq \calm$ is an inclusion of type

${\rm II}_1$ factors of finite index on a separable Hilbert space, and if

$\caln$ has a Cartan subalgebra then we show that

$H^n(\caln, \calm) = 0$ for

$n\ge 1$ . We also show that

$H^n_{\rm cb}(\caln, \calm)= 0$ ,

$n\ge 1$ , for an arbitrary finite index inclusion

$\caln \subseteq \calm$ of von~Neumann algebras.

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