2002/11/15 by Menassie Ephrem, Ephrem, Menassie · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Spectral Theory in Mathematical Physics #math.OA #msc:46L05 #msc:46L35 #msc:46L55
paper · pdf · doi:10.48550/arxiv.math/0211241
20 pages
arxiv created 2003/04/01 · arxiv updated 2009/11/30
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.