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# Pure Infiniteness of the Crossed Product of an AH-Algebra by an Endomorphism

Published:2011-10-22
Printed: Jun 2012
• Klaus Thomsen,
Institut for matematiske fag, Ny Munkegade, 8000 Aarhus C, Denmark
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## Abstract

It is shown that simplicity of the crossed product of a unital AH-algebra with slow dimension growth by an endomorphism implies that the algebra is also purely infinite, provided only that the endomorphism leaves no trace state invariant and takes the unit to a full projection.
 Keywords: purely infinite $C^*$-algebras, crossed products
 MSC Classifications: 46-xx - unknown classification 46-xx