Groupoid and Inverse Semigroup Presentations of Ultragraph C^*-Algebras

2007/09/14 by Alberto E. Marrero, Marrero, Alberto, Paul S. Muhly +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0709.2281

Abstract

Inspired by the work of Paterson on C^∗-algebras of directed graphs, we show how to associate a groupoid \mathfrakG_G to an ultragraph G in such a way that the C^*-algebra of \mathfrakG_G is canonically isomorphic to Tomforde's C^*-algebra C^*(G). The groupoid \mathfrakG_G is built from an inverse semigroup S_G naturally associated to G.

Citations

• Ultragraph C*-algebras via topological quivers

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