Characterizing Liminal And Type I Graph C*-Algebras

الأصل · EN

We prove that the C*-algebra of a directed graph E is liminal iff the graph satisfies the finiteness condition: if p is an infinite path or a path ending with a sink or an infinite emitter, and if v is any vertex, then there are only finitely many paths starting with v and ending with a vertex in p. Moreover, C*(E) is Type I precisely when the circuits of E are either terminal or transitory, i.e., E has no vertex which is on multiple circuits, and E satisfies the weaker condition: for any infinite path λ, there are only finitely many vertices of λ that get back to λ in an infinite number of ways.