Graph inverse semigroups: their characterization and completion
Graph inverse semigroups: their characterization and completion
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DOI：
10.1016/j.jalgebra.2014.04.001
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发表时间：
2011-06
期刊：
影响因子：
--
通讯作者：
David G. Jones;M. Lawson
中科院分区：
文献类型：
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作者：
David G. Jones;M. Lawson
图逆半群推广了多环逆半群，在C -代数理论中占有重要地位。在本文中，我们刻画了这样的半群，并证明了在适当的条件下，它们是如何被补全的，从而形成我们称之为图的Cuntz-Krieger半群。证明了该半群是与图相关联的拓扑群的充裕半群，是图的Leavitt路径代数的半群模拟。
Graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C⁎-algebras. In this paper, we characterize such semigroups and show how they may be completed, under suitable conditions, to form what we call the Cuntz–Krieger semigroup of the graph. This semigroup is proved to be the ample semigroup of a topological groupoid associated with the graph, and the semigroup analogue of the Leavitt path algebra of the graph.