Abstract |
The most elementary C*-algebras are the unital abelian ones, and these form
the only class to be completely classified. They are the algebras of continuous functions
on compact Hausdorff spaces. A different way to describe these algebras is to say that
all of their irreducible representations are one-dimensional, and in this way there is a
natural generalization: those algebras whose irreducible representations are all of the
same finite dimension. These are called the homogeneous C*-algebras, an example of
which would be the algebra C([0,1],M_2) of continuous functions on the unit interval
with values in the 2x2 matrices. However, they can be much more complicated than
this. Using elementary linear algebra, we will introduce an isomorphism invariant for
these algebras, and will show how to calculate this using some beautiful theorems from
algebraic topology.
This talk is designed for a wide audience, and all terms above will be explained.
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