Simple labeled graph C*-algebras are associated to disagreeable labeled spaces

摘要

By a labeled graph C*-algebra we mean a C*-algebra associated to a labeled space (E, L, epsilon) consisting of a labeled graph (E, L) and the smallest normal accommodating set epsilon of vertex subsets. Every graph C*-algebra C* (E) is a labeled graph C*-algebra and it is well known that C* (E) is simple if and only if the graph E is cofinal and satisfies Condition (L). Bates and Pask extend these conditions of graphs E to labeled spaces, and show that if a set-finite and receiver set-finite labeled space (E, L, epsilon) is cofinal and disagreeable, then its C*-algebra C* (E, L, epsilon) is simple. In this paper, we show that the converse is also true. (C) 2018 Elsevier Inc. All rights reserved.