A class of $C^*$-algebras generalizing both graph algebras and homeomorphism $C^*$-algebras IV, pure infiniteness

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76354This is the final one in the series of papers where we introduce and study the $C^*$-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated $C^*$-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as $C^*$-algebras associated with topological graphs.28 pagesOperator AlgebrasPrimary 46L05; Secondary 46L55, 37B99A class of $C^*$-algebras generalizing both graph algebras and homeomorphism $C^*$-algebras IV, pure infinitenesstext