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Jan Hendrik Bruinier, Darmstadt Editorial Board, Valentin Blomer, Chantal David, Manfred Droste, Frank Duzaar, Siegfried Echterhoff, Jan Frahm, Maria Aarhus, Clara Storrs

Abstract

In this paper, we introduce a new technique in the study of the *{*}-regular closure of some specific group algebras KG inside 𝒰⁢(G){{\mathcal{U}}(G)}, the *{*}-algebra of unbounded operators affiliated to the group von Neumann algebra 𝒩⁢(G){{\mathcal{N}}(G)}. The main tool we use for this study is a general approximation result for a class of crossed product algebras of the form CK⁢(X)⋊Tℤ{C_{K}(X)\rtimes_{T}{\mathbb{Z}}}, where X is a totally disconnected compact metrizable space, T is a homeomorphism of X , and CK⁢(X){C_{K}(X)} stands for the algebra of locally constant functions on X with values on an arbitrary field K . The connection between this class of algebras and a suitable class of group algebras is provided by the Fourier transform. Utilizing this machinery, we study an explicit approximation for the lamplighter group algebra. This is used in another paper by the authors to obtain a whole family of ℓ2{\ell^{2}}-Betti numbers arising from the lamplighter group, most of them transcendental.

Locations

• Forum Mathematicum - View - PDF