Graph inverse semigroups: their characterization and completion

By David G. Jones, Mark V. Lawson. 2011

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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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/30c101fccbf428eb757816b8e90ee288345ee316