Speaker: Dr. Trent Yeend (University of Newcastle)

Title: Three Approaches to Graph Algebras

Date: Tuesday, 8 August 2006
Time: 2:00 pm
Venue: RC-4082, The Red Centre, UNSW

Graph algebras' is the term used to describe C*-algebras which
contain particular types of representations of directed graphs.
When studying the structure theory of graph algebras, we focus
on the universal objects for the representations. That is, given
a directed graph E = (E0,E1,r,s), there is a C*-algebra C*(E) such
that any Cuntz-Krieger representation of E in a C*-algebra B gives
a canonical homomorphism pi from C^*(E) to B.

If E has countable vertex and edge sets, C*(E) is generated by a
family of partial isometries, and it is profitable to analyze the
structure of C*(E) directly using these elements. However, in general
we wish to consider directed graphs for which the vertex and edge sets
are locally compact Hausdorff spaces, and as a consequence we cannot
expect C*(E) to contain any partial isometries. So we look for
different ways to study C*(E); one way is through the use of groupoids,
and another is through the use of Hilbert bimodules. These alternate
approaches not only lend themselves to the extra generality, but
also give us a way of viewing familiar C*-algebras as graph algebras.

In this seminar, these concepts and approaches will be discussed
along with examples to distinguish them.