Non-amenable tight squeezes by Kirchberg algebras

Purely infinite C*-algebras arising from crossed products

We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a commutative C*-algebra, where our sufficient conditions can be phrased in terms of paradoxicality of subsets of the spectrum of the abelian C*-algebra. As an application of our results we show that every discrete countable non-amenable exact group admits a free amenable minimal action on the Cantor set such that the corresponding crossed product C*-algebra is…

Razak-Jacelon代数的等变Kirchberg-Phillips型吸收

Equivariant Kirchberg-Phillips type absorption for the Razak-Jacelon algebra

本文证明简单可分核单调迹C*-代数上的强外顺从群作用在张量Razak-Jacelon代数后具有余循环共轭的唯一性，并用中心序列代数的不动点子代数给出刻画。

Non-supramenable groups acting on locally compact spaces

Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UCT class are constructed using crossed products for both amenable and non-amenable groups.

Nuclearity and Exactness for Groupoid Crossed Products

Let $(\mathcal{A}, G, α)$ be a groupoid dynamical system. We show that if $G$ is assumed to be measurewise amenable and the section algebra $A = Γ_0(G^{(0)}, \mathcal{A})$ is nuclear, then the associated groupoid crossed product is also nuclear. This generalizes an earlier result of Green for crossed products by locally compact groups. We also extend a related result of Kirchberg to groupoids. In particular, if $A$ is exact and $G$ is amenable, then we show that $\mathcal{A} \rtimes G$ is exact.

Some Results on Matricial Field C-Algebras

In this paper, we consider Blackadar and Kirchberg's MF algebras. We show that any inner quasidiagonal C-algebra is MF algebra and we generalize Voiculescu's Representation Theorem for a special version of MF algebras. Moreover, we define a weak version of MF algebras namely matrical amenable (AM) algebras, and prove some results related to this new notion. Finally, we consider real C-algebras and we show that a real C-algebra is MF if and only if its complexification is MF.

Inner amenability and approximation properties of locally compact quantum groups

We introduce an appropriate notion of inner amenability for locally compact quantum groups, study its basic properties, related notions, and examples arising from the bicrossed product construction. We relate these notions to homological properties of the dual quantum group, which allow us to generalize a well-known result of Lau--Paterson, resolve a recent conjecture of Ng--Viselter, and prove that, for inner amenable quantum groups $\mathbb{G}$, approximation properties of the dual operator algebras can be averaged to approximation properties $\mathbb{G}$. Similar homological techniques are …

顺从 C*-代数的抽象分类定理

Abstract classification theorems for amenable C*-algebras

本文介绍顺从 C*-代数的单位分类定理及其历史背景，并提出一种与冯·诺依曼代数结果直接相连的抽象分类方法，无需在 C*-代数内部构造逼近结构。

Rigid sides of approximately finite dimensional simple operator algebras in non-separable category

Applying Popa's orthogonality method to a new class of groups, we construct amenable group factors which are prime and have no infinite dimensional regular abelian *-subalgebras. By adjusting Farah--Katsura's solution of Dixmier's problem to the von Neumann algebra setting, we obtain the first examples of prime AFD factors and tensorially prime simple AF-algebras. Our results are proved in ZFC, thus in particular answering questions asked by Farah--Hathaway--Katsura--Tikuisis. We also directly determine central sequences of certain crossed products. This concludes the failure of the Kirchberg …

完全正逼近与归纳系统

Completely positive approximations and inductive systems

本文提出C*-编码条件刻画归纳系统极限完全序同构于C*-代数，并证明可分核C*-代数恰为C*-编码系统极限，推广了NF与CPC*-系统，为所有可分核C*-代数提供无零阶映射的归纳极限描述。