Graph products for groups were defined by Green in her thesis  as a generalization of both Cartesian and free products. In this paper we define the corresponding graph product for reduced and maximal -algebras, von Neumann algebras and quantum groups. We prove stability properties including permanence of II-factors, the Haagerup property, exactness and, under suitable conditions, the property of rapid decay for quantum groups.
Cite this article
Martijn Caspers, Pierre Fima, Graph products of operator algebras. J. Noncommut. Geom. 11 (2017), no. 1, pp. 367–411DOI 10.4171/JNCG/11-1-9