1.Department of Mathematics and Statistics,University of Otago,Dunedin,New Zealand
Abstract:
There are many different crossed products by an endomorphism of a C*-algebra, and constructions by Exel and Stacey have proved particularly useful. Here we consider Exel crossed products associated
to transfer operators which extend to be unital on the multiplier algebra. We show that every Exel crossed product is isomorphic
to a Stacey crossed product, though by a different endomorphism of a different C*-algebra. We apply this result to a variety of Exel systems, including those associated to shifts on the path spaces of directed
graphs.