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

Abstract

We investigate factoriality, Connes' type $\mathrm{III}$ 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 $\mathrm{III}$ invariants.

31 pages

References in corpus (5)

• Amenable absorption in amalgamated free product von Neumann algebras
• Classification of a family of non almost periodic free Araki-Woods factors
• Strongly ergodic equivalence relations: spectral gap and type III invariants
• Fullness and Connes' $\mathbf{\tau }$ invariant of type III tensor product factors
• Unique prime factorization for infinite tensor product factors

Cited by in corpus (3)

• Structure of extensions of free Araki-Woods factors
• Fullness of crossed products of factors by discrete groups
• Strong primeness for equivalence relations arising from Zariski dense subgroups