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On a construction of unitary cocycles and the representation theory of amenable groups

Published online by Cambridge University Press:  19 September 2008

Colin E. Sutherland
Colin E. Sutherland
Affiliation:
Department of Mathematics, University of New South Wales, P.O. Box 1, Kensington, New South Wales, Australia2033
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Abstract

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If K is a countable amenable group acting freely and ergodically on a probability space (Γ, μ), and G is an arbitrary countable amenable group, we construct an injection of the space of unitary representations of G into the space of unitary 1-cocyles for K on (Γ, μ); this injection preserves intertwining operators. We apply this to show that for many of the standard non-type-I amenable groups H, the representation theory of H contains that of every countable amenable group.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 1 , March 1983 , pp. 129 - 133
Copyright
Copyright © Cambridge University Press 1983

References

REFERENCES

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