Stacey crossed products associated to Exel systems

TL;DR

This paper demonstrates that all Exel crossed products can be represented as Stacey crossed products with different endomorphisms and C*-algebras, unifying various constructions and applying to systems like graph shifts.

Contribution

It proves the isomorphism between Exel and Stacey crossed products, providing a unified framework for analyzing these constructions.

Findings

Exel crossed products are isomorphic to Stacey crossed products.

The result applies to systems related to shifts on graph path spaces.

Unification of different crossed product constructions in C*-algebra theory.

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 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.