2018/04/03 by Austin, Kyle, Mitra, Atish
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1804.00967
We construct a large class of morphisms, which we call partial morphisms, of groupoids that induce *-morphisms of maximal and minimal groupoid C^*-algebras. We show that the association of a groupoid to its maximal (minimal) groupoid C^*-algebra and the association of a partial morphism to its induced morphism are functors (both of which extend the Gelfand functor). We show how to geometrically visualize lots of *-morphisms between groupoid C^*-algebras. As an application, we construct a groupoid models of the entire inductive systems of the Jiang-Su algebra Z and the Razak-Jacelon algebra W.