A new family of ambient C*-algebras around graph products yields universal properties, nuclearity/exactness characterizations, a maximal ideal, and new simplicity and trace-uniqueness criteria for graph product C*-algebras.
Anantharaman-Delaroche, On tensor products of group C ∗-algebras and related topics , Limits of graphs in group theory and computer science, 1-35, EPFL Press, Lausanne, 2009
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Universal C$^{\ast}$-Algebras from Graph Products: Structure and Applications
A new family of ambient C*-algebras around graph products yields universal properties, nuclearity/exactness characterizations, a maximal ideal, and new simplicity and trace-uniqueness criteria for graph product C*-algebras.