THE ÉTALE GROUPOID OF AN INVERSE SEMIGROUP AS A GROUPOID OF FILTERS
THE ÉTALE GROUPOID OF AN INVERSE SEMIGROUP AS A GROUPOID OF FILTERS
复制标题
作为滤波器群的反半群的 ÉTALE 群
DOI：
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发表时间：
2011
影响因子：
0.7
通讯作者：
B. Steinberg
中科院分区：
文献类型：
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作者：
M. Lawson;S. Margolis;B. Steinberg
摘要Paterson展示了如何利用泛函分析的思想从逆半群构造étale型群胚。这种结构后来被Lenz简化了。我们证明了Lenz的构造本身可以通过滤子进一步简化：与逆半群相关的拓扑广群恰恰是滤子的群群。另外，幂等滤子是闭逆子半群，因此通过部分双射确定传递表示。利用滤子和部分双射表示之间的这种联系，证明了逆半群的线性表示可以从出现在相关拓扑群中的群构造出来。
Abstract Paterson showed how to construct an étale groupoid from an inverse semigroup using ideas from functional analysis. This construction was later simplified by Lenz. We show that Lenz’s construction can itself be further simplified by using filters: the topological groupoid associated with an inverse semigroup is precisely a groupoid of filters. In addition, idempotent filters are closed inverse subsemigroups and so determine transitive representations by means of partial bijections. This connection between filters and representations by partial bijections is exploited to show how linear representations of inverse semigroups can be constructed from the groups occurring in the associated topological groupoid.