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University of Wollongong

2004

Science and Technology Studies

Algebras

Articles 1 - 2 of 2

Full-Text Articles in Social and Behavioral Sciences

Cuntz-Krieger Algebras Of Infinite Graphs And Matrices, Iain Raeburn, Wojciech Szymanski Jan 2004

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 Jan 2004

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 …