The primitive ideal space of the C*-algebras of infinite graphs

Abstract

Abstract. For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C ∗ (E). The primary purpose of this article is to give a description of the primitive ideal space of the C ∗-algebra C ∗ (E) corresponding to an arbitrary countable directed graph E. The two main results of the article, Theorem 2.10 (together with Corollary 2.11) and Theorem 3.4, identify elements of Prim(C ∗ (E)) and describe the closure operation in the hull-kernel topology. These