论文标题
Ampurysoid代数，痕迹和应用的稳定有限性
Stable finiteness of ample groupoid algebras, traces and applications
论文作者
论文摘要
在本文中，我们研究了稳定的群体素代代数的稳定有限性，并应用于逆半群代数和莱维特路径代数，恢复了旧结果并证明了一些新结果。此外，我们开发了一种（忠实的）痕迹在ampimoid代数上，模仿$ c^\ ast $ -Algebra理论，但利用了我们的功能很简单，因此即使在非Hausdorff设置中也没有集成性问题。痕迹理论与布尔逆半群的不变理论密切相关。我们包括有关更一般的半群代数的稳定有限的附录，改善了蒙恩的早期结果，蒙恩的较早结果与本文的其余部分无关。
In this paper we study stable finiteness of ample groupoid algebras with applications to inverse semigroup algebras and Leavitt path algebras, recovering old results and proving some new ones. In addition, we develop a theory of (faithful) traces on ample groupoid algebras, mimicking the $C^\ast$-algebra theory but taking advantage of the fact that our functions are simple and so do not have integrability issues, even in the non-Hausdorff setting. The theory of traces is closely connected with the theory of invariant means on Boolean inverse semigroups. We include an appendix on stable finiteness of more general semigroup algebras, improving on an earlier result of Munn, which is independent of the rest of the paper.
