This article is cited in 37 papers

Cohomology of groups in unitary representations, the neighborhood of the identity, and conditionally positive definite functions

A. M. Vershik, S. I. Karpushev


Abstract: It is shown that every irreducible unitary representation of a locally compact separable group with nontrivial first cohomology is unseparable from the identity representation in the space of irreducible unitary representations. For compactly generated groups the statement can be sharpened: a nontrivial cocycle in such a representation is in a certain sense the limit of trivial cocycles in irreducible representations. A survey is given of the connections between the notions indicated in the title.
Bibliography: 17 titles.

UDC: 512.86

MSC: 22D10

Received: 25.12.1981

 English version: Mathematics of the USSR-Sbornik, 1984, 47:2, 513–526

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