English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

Group cocycles and the ring of affiliated operators