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# Purely infinite, simple $C^\ast$-algebras arising from free product constructions

Published:1998-04-01
Printed: Apr 1998
• Kenneth J. Dykema
• Mikael Rørdam
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## Abstract

Examples of simple, separable, unital, purely infinite $C^\ast$-algebras are constructed, including: \item{(1)} some that are not approximately divisible; \item{(2)} those that arise as crossed products of any of a certain class of $C^\ast$-algebras by any of a certain class of non-unital endomorphisms; \item{(3)} those that arise as reduced free products of pairs of $C^\ast$-algebras with respect to any from a certain class of states.
 MSC Classifications: 46L05 - General theory of $C^*$-algebras 46L45 - Decomposition theory for $C^*$-algebras