Factoriality, Connes' type III invariants and fullness of amalgamated free product von Neumann algebras

We investigate factoriality, Connes’ type $\mathrm{I}\mathrm{I}\mathrm{I}$ invariants and fullness of arbitrary amalgamated free product von Neumann algebras using Popa’s deformation/rigidity theory. Among other things, we generalize many previous structural results on amalgamated free product von Neumann algebras and we obtain new examples of full amalgamated free product factors for which we can explicitely compute Connes’ type $\mathrm{I}\mathrm{I}\mathrm{I}$ invariants.