Group cocycles and the ring of affiliated operators

Details Group cocycles and the ring of affiliated operators Group cocycles and the ring of affiliated operators

2007-08-31

arxiv.org/abs/0708.4327v2

Mathematics

Group Theory

24 pages, no figures

Scientific paper

In this article we study cocycles of discrete countable groups with values in l^2(G) and the ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with coefficients in l^2(G) and answer several questions from [CTV]. Moreover, we obtain strong results about the existence of free subgroups and the subgroup structure, provided the group has a positive first l^2-Betti number. We give numerous applications and examples of groups which satisfy our assumptions.

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