层中系数的Étale广群代数与斜逆半群环
Étale groupoid algebras with coefficients in a sheaf and skew inverse semigroup rings
摘要：
给定逆半群$S$在环$A$上的作用$φ$（$φ(s)$的定义域记为$D_{s^*}$），证明了若$D_e$的理想是酉的，且$e$是幂等元，则斜逆半群环$A\rtimes S$可实现为环层中系数的充要群胚的卷积代数.相反，我们证明了环层中系数为零的充分广群的卷积代数同构于这类斜逆半群环。我们恢复已知的结果在文献中的Steinberg代数域作为特殊情况。
英文摘要：
Given an action $φ$ of of inverse semigroup $S$ on a ring $A$ (with domain of $φ(s)$ denoted by $D_{s^*}$) we show that if the ideals $D_e$, with $e$ an idempotent, are unital, then the skew inverse semigroup ring $A\rtimes S$ can be realized as the convolution algebra of an ample groupoid with coefficients in a sheaf of rings. Conversely, we show that the convolution algebra of an ample groupoid with coefficients in a sheaf of rings is isomorphic to a skew inverse semigroup ring of this sort. We recover known results in the literature for Steinberg algebras over a field as special cases.
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