Pure infiniteness of the crossed product of an AH-algebra by an endomorphism

TL;DR

This paper proves that under certain conditions, the crossed product of a unital AH-algebra with slow dimension growth by an endomorphism is purely infinite, expanding understanding of the structure of such C*-algebras.

Contribution

It establishes conditions under which the crossed product of a unital AH-algebra by an endomorphism is purely infinite, specifically when the algebra is simple and the endomorphism meets certain criteria.

Findings

Crossed product is purely infinite under specified conditions.

Requires the algebra to be simple and have slow dimension growth.

Endomorphism must not leave a trace invariant and must map the unit to a full projection.

Abstract

It is shown that the crossed product of a unital AH-algebra with slow dimension growth by an endomorphism is purely infinite when it is simple, provided the endomorphism does not leave a trace state invariant and maps the unit to a full projection.