Computing K-theory and Ext for graph C*-algebras

计算分类强自吸收C*代数丛的上同调群

Computing cohomology groups that classify bundles of strongly self-absorbing $C^*$-algebras

本文研究了强自吸收C*代数丛的上同调群，通过普通上同调和连通K-理论计算，并开发了复杂周期拓扑K-理论单位谱的唯一性结果。

Computing Ext for graph algebras

For a row-finite graph G with no sinks and in which every loop has an exit, we construct an isomorphism between Ext(C*(G)) and coker(A-I), where A is the vertex matrix of G. If c is the class in Ext(C*(G)) associated to a graph obtained by attaching a sink to G, then this isomorphism maps c to the class of a vector which describes how the sink was added. We conclude with an application in which we use this isomorphism to produce an example of a row-finite transitive graph with no sinks whose associated C*-algebra is not semiprojective.

关于计算 C*-代数的 Grothendieck 环的注记

Remarks on computing the Grothendieck rings of C*-algebras

本文将 Grothendieck 构造调整适用于 C*-代数，通过探讨非平凡特征的存在性，研究了特定 C*-代数具有非平凡 Grothendieck 环的条件，并详细分析了 $\mathbb{C}$、$\mathbb{R}$ 和 $\mathbb{H}$ 上的代数环。

$C^*$-algebras of labelled graphs III - $K$-theory computations

In this paper we give a formula for the $K$-theory of the $C^*$-algebra of a weakly left-resolving labelled space. This is done by realising the $C^*$-algebra of a weakly left-resolving labelled space as the Cuntz-Pimsner algebra of a $C^*$-correspondence. As a corollary we get a gauge invariant uniqueness theorem for the $C^*$-algebra of any weakly left-resolving labelled space. In order to achieve this we must modify the definition of the $C^*$-algebra of a weakly left-resolving labelled space. We also establish strong connections between the various classes of $C^*$-algebras which are assoc…