A Class of Limit Algebras Associated with Directed Graphs
2007 ◽
Vol 82
(3)
◽
pp. 345-368
◽
Keyword(s):
AbstractEvery directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C* -algebras. We prove the algebras generated by all shifts of a fixed period are of Cuntz-Krieger and Toeplitz-Cuntz-Krieger type. The limit C* -algebras determined by an increasing sequence of positive integers, each dividing the next, are proved to be isomorphic to Cuntz-Pimsner algebras and the linking maps are shown to arise as factor maps. We derive a characterization of simplicity and compute the K-groups for these algebras. We prove a classification theorem for the class of algebras generated by simple loop graphs.
1986 ◽
Vol 24
(1-3)
◽
pp. 53-69
◽
Keyword(s):
Keyword(s):
Keyword(s):
2012 ◽
Vol 09
(02)
◽
pp. 1260005
◽
1994 ◽
Vol 135
(1-3)
◽
pp. 335-347
◽
Keyword(s):