On the lack of inverses to C*-extensions related to property T groups

The universal property of inverse semigroup equivariant $KK$-theory

Higson proved that every homotopy invariant, stable and split exact functor from the category of $C^*$-algebras to an additive category factors through Kasparov's $KK$-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup equivariant setting.

精确性与具有逼近性质的Fell包 over逆半群

Exactness and Fell bundles with the approximation property over inverse semigroups

本文研究了具有逼近性质的Fell包 over逆半群的减少横截代数的精确性，证明其等价于Fell包的单位纤维的精确性，并扩展了作者关于局部紧豪斯多夫第二可数群oid作用于可分C*-代数的结果。

逆半群与非豪斯多夫群胚上 Fell 丛的逼近性质

Approximation properties of Fell bundles over inverse semigroups and non-Hausdorff groupoids

本文在逆半群上 Fell 丛的框架下证明 Fell 吸收技巧的类比，并利用 Exel 逼近性质证明全截面与约化截面 C*-代数同构，进而得到具有逼近性质且单位纤维为核的 Fell 丛的截面 C*-代数是核的，且结果同样适用于 étale 非豪斯多夫群胚。

Inverse limits of rings and Multiplier rings

It is proved that the exchange property, the Bass stable rank and the quasi-Bass property are all preserved under surjective inverse limits. This is then applied to multiplier rings by showing that in many cases can be obtained as inverse limits.

(b c) 逆的广义 EP 性质

Generalized EP properties of (b c) inverses

研究在 * - 巴拿赫代数框架内广义 (b,c) EP 逆的概念，通过相关分解、广义 Drazin 逆等给出其特征刻画，呈现极型性质，揭示其与广义群逆反序律联系。

Graph products and the absence of property (AR)

We discuss the internal structure of graph products of right LCM semigroups and prove that there is an abundance of examples without property (AR). Thereby we provide the first examples of right LCM semigroups lacking this seemingly common feature. The results are particularly sharp for right-angled Artin monoids.