# Extensions of graph C*-algebras

## Ph.D. Thesis

**ABSTRACT:** We consider C*-algebras associated to row-finite
(directed)
graphs and examine the effect that adding a sink to the graph
has on the associated C*-algebra. In
Chapter 2 we give a precise definition of how
a sink may be added to a graph, and discuss a notion of
equivalence of C*-algebras if this is done in two different
ways. We also define operations that may be
performed on these graphs and then use these operations to
determine equivalence of the associated C*-algebras in
certain circumstances. In Chapters 3 and 4 we discuss the Ext functor and
show that adding a sink to a graph G determines an element c of Ext
(C*(G)). With this in mind, we construct an isomorphism w : Ext
(C*(G)) -> coker (A-I), where A is the
vertex matrix of G. We also show that the value
that w assigns to c is the class of a vector describing
how the sink was added to G. In Chapter 5 we
use this isomorphism to strengthen the results of
Chapter 2. In particular, if two graphs are formed by adding a sink to G,
then we give conditions for their associated C*-algebras to be equivalent
in terms of the vectors describing how the sinks were added.

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The material in this thesis has been rewritten for publication in the
following three papers.

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