Rigidity for von Neumann algebras of graph product groups, I: Structure of automorphisms

We study various rigidity aspects of the von Neumann algebra L( ), where is a graph product group whose underlying graph is a certain cycle of cliques and the vertex groups are wreath-like product property (T) groups.Using an approach that combines methods from Popa's deformation/rigidity theory with new techniques pertaining to graph product algebras, we describe all symmetries of these von Neumann algebras and reduced C * -algebras by establishing formulas in the spirit of Genevois and Martin's results on automorphisms of graph product groups.