New C*‐completions of discrete groups and related spaces

By N. Brown, Erik P. Guentner. 2012

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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].

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Citations in the corpus

Annular representation theory for rigid $C^{*}$-tensor categories (2015, methodology): “ understood as resulting from the composition of cp-multipliers as in the proof of Proposition 5.3 in [38]. We proceed to dene universal norms with respect to certain ideals of ‘1(Irr(C)), following [7]. 36 SHAMINDRA KUMAR GHOSH AND COREY JONES Consider the annular centralizer algebra of weight k2, ”
Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture (2013, background): “now see that µ(f) = µ(g◦ f). The result now follows. It is well known that the boundary groupoid associated to a box space Γ decomposes as ∂β Γ⋊Γ, for a proof see [9]. We now recall Corollary 5.12 of [4]: Proposition 39. Let Γ be a discrete group acting on a space Xwith an invariant probablity measu”
The Haagerup property for locally compact quantum groups (2013, result): “Property (ii) can also be compared with recent work of Brown and Guentner [16], who characterise the Haagerup property for a discrete group in terms of the equality of the “C0-completion” of the complex group algebra and the full group C -algebra, i.”