The structure of crossed products by endomorphisms

TL;DR

This paper characterizes when Stacey crossed products are simple or purely infinite, using endomorphism conditions and graph C*-algebra representations, advancing understanding of their ideal structure.

Contribution

It provides new criteria for simplicity and pure infiniteness of Stacey crossed products via endomorphism and graph algebra techniques.

Findings

Simplicity of Stacey crossed products characterized by endomorphism conditions.

Graph C*-algebras are represented as Stacey crossed products, linking their ideal properties.

Sufficient conditions for pure infiniteness of Stacey crossed products established.

Abstract

We describe simplicity of the Stacey crossed product A\times_\beta \N in terms of conditions of the endomorphism \beta. Then, we use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product C*(E)^\gamma\times_{\beta_E}\N to study its ideal properties, in terms of the (non-classical) C*-dynamical system (C*(E)^\gamma, \beta_E). Finally, we give sufficient conditions for the Stacey crossed product A\times_\beta \N being a purely infinite simple C*-algebra.