**
Jaspar
Wiart,
Department
of
Pure
Math,
University
of
Waterloo**

“Operator
algebras
arising
from
number
theory.”

We begin by discussing the Toeplitz algebra of the ax+b-semigroup of a number ring. This C*-algebra can be described as a universal C*-algebra defined using generators and relations. We explain how these generators and relations recover the structure of the Toeplitz algebra. This C*-algebra is also the C*-envelope of the semicrossed product of a certain dynamical system arising from number theory. We give the dynamical system, sketch the proof of the isomorphism, state the main dilation theorem, and give an example.

MC 5413