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Full-Text Articles in Social and Behavioral Sciences
Cuntz-Krieger Algebras Of Infinite Graphs And Matrices, Iain Raeburn, Wojciech Szymanski
Cuntz-Krieger Algebras Of Infinite Graphs And Matrices, Iain Raeburn, Wojciech Szymanski
Faculty of Engineering and Information Sciences - Papers: Part A
We show that the Cuntz-Krieger algebras of infinite graphs and infinite {0,1}-matrices can be approximated by those of finite graphs. We then use these approximations to deduce the main uniqueness theorems for Cuntz-Krieger algebras and to compute their K-theory. Since the finite approximating graphs have sinks, we have to calculate the K-theory of Cuntz-Krieger algebras of graphs with sinks, and the direct methods we use to do this should be of independent interest.
Classification Theorems For The C*-Algebras Of Graphs With Sinks, Iain Raeburn, Mark Tomforde, Dana Williams
Classification Theorems For The C*-Algebras Of Graphs With Sinks, Iain Raeburn, Mark Tomforde, Dana Williams
Faculty of Engineering and Information Sciences - Papers: Part A
We consider graphs E which have been obtained by adding one or more sinks to a fixed directed graph G. We classify the C*-algebra of E up to a very strong equivalence relation, which insists, loosely speaking, that C*(G) is kept fixed. The main invariants are vectors WE: G0 → which describe how the sinks are attached to G; more precisely, the invariants are the classes of the WE in the cokernel of the map A – I, where A is the adjacency matrix of the graph …