%0 Journal Article
%T Graph inverse semigroups: their characterization and completion
%A David G. Jones
%A Mark V. Lawson
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1106.3644v2