New C*-completions of discrete groups and related spaces

Nathanial P. Brown, Erik P. Guentner

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


Let Γ be a discrete group. To every ideal in ℓ (Γ), we associate a C*-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general framework we develop unifies some classical results and leads to new insights. For example, we give the first C*-algebraic characterization of a-T-menability; a new characterization of property (T); new examples of 'exotic' quantum groups; and, after extending our construction to transformation groupoids, we improve and simplify a recent result of Douglas and Nowak ['Hilbert C*-modules and amenable actions', Studia Math. 199 (2010) 185-197].

Original languageEnglish (US)
Pages (from-to)1181-1193
Number of pages13
JournalBulletin of the London Mathematical Society
Issue number6
StatePublished - Dec 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics


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