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arXiv · 1106.3644

Graph inverse semigroups: their characterization and completion

David G. Jones·Mark V. Lawson
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Abstract

Graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C*-algebras. This paper has two main goals: first, to provide an abstract characterization of graph inverse semigroups; and second, to show how they may be completed, under suitable conditions, to form what we call the Cuntz-Krieger semigroup of the graph. This semigroup is the ample semigroup of a topological groupoid associated with the graph, and the semigroup analogue of the Leavitt path algebra of the graph.

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David G. Jones, Mark V. Lawson. 2013-08-13. Graph inverse semigroups: their characterization and completion. https://arxiv.org/abs/1106.3644

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