Primitive Ultragraph C*-algebras

Primitive Ultragraph C*-algebras

In this note, we consider the primitivity of ultragraph C*--algebras. Ultragraphs and their C*-algebras were introduced by Mark Tomforde in 2003 for giving an specific generalization of the class of graph C*-algebras. We may characterize all primitive ultragraph C*-algebras by showing that an ultragraph C*--algebra C(G) is primitive if and only if the underlying ultragraph G satisfies condition (L) and downward property.