（非）奇异完备化：迷向群群代数的群代数

étale群胚的exotic $\ m C^*$-完备化

Exotic $\rm C^*$-completions of étale groupoids

本文将离散群的理想完备化推广至étale群胚，构造了一类新的$\ m C^*$-代数，并揭示了其与Haagerup性质的联系，证明了某些群胚存在大量exotic $\ m C^*$-代数。

约化群胚C*-代数简单性的刻画

A characterization of simplicity of reduced groupoid C*-algebras

本文刻画了约化群胚C*-代数的简单性，证明其等价于存在余稠密单位点集具有C*-简单迷向群，并构造反例回答Christensen和Neshveyev的问题。

与双群胚相关的奇异群胚 C*-代数

Exotic groupoid $C^*$-algebras associated to double groupoids

本文研究由子群对构造的双群胚，证明当部分作用群具有 Brown–Guentner 奇异理想完备化时，étale 双群胚也相应具有奇异 C*-完备化。

Exotic coactions

If a locally compact group G acts on a C*-algebra B, we have both full and reduced crossed products, and each has a coaction of G. We investigate "exotic" coactions in between, that are determined by certain ideals E of the Fourier-Stieltjes algebra B(G) -- an approach that is inspired by recent work of Brown and Guentner on new C*-group algebra completions. We actually carry out the bulk of our investigation in the general context of coactions on a C*-algebra A. Buss and Echterhoff have shown that not every coaction comes from one of these ideals, but nevertheless the ideals do generate a wid…

New C*-completions of discrete groups and related spaces

Let $Γ$ be a discrete group. To every ideal in $\ell^{\infty}(\G)$ 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 Now…

Exotic Ideals in Free Transformation Group $C^*$-Algebras

Let $Γ$ be a discrete group acting freely via homeomorphisms on the compact Hausdorff space $X$ and let $C(X) \rtimes_ηΓ$ be the completion of the convolution algebra $C_c(Γ,C(X))$ with respect to a $C^*$-norm $η$. A non-zero ideal $J \unlhd C(X) \rtimes_ηΓ$ is exotic if $J \cap C(X) = \{0\}$. We show that exotic ideals are present whenever $Γ$ is non-amenable and there is an invariant probability measure on $X$. This fact, along with the recent theory of exotic crossed product functors, allows us to provide answers to two questions of K. Thomsen. Using the Koopman representation and a recent …