On the Cohomology of Actions of Groups by Bernoulli Shifts

Details On the Cohomology of Actions of Groups by Bernoulli Shifts On the Cohomology of Actions of Groups by Bernoulli Shifts

2003-10-15

arxiv.org/abs/math/0310211v2

Mathematics

Operator Algebras

9 pages; some corrections in Lemma 3.2 (Dec. 18, 2003), 10 pages

Scientific paper

We prove that if $G$ is a countable, discrete group having infinite, normal
subgroups with the relative property (T), then the Bernoulli shift action of
$G$ on ${\underset g \in G \to \Pi} (X_0, \mu_0)_g$ for $(X_{0},\mu_{0})$ an
arbitrary probability space, has first cohomology group isomorphic to the
character group of $G$.

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