Free products of finite dimensional and other von

The von Neumann algebra free product of arbitary finite dimensional von Neumann algebras with respect to arbitrary faithful states, at least one of which is not a trace, is found to be a type III factor possibly direct sum a finite dimensional algebra. The free product state on the type III factor is what we call an extremal almost periodic state, and has centralizer isomorphic to L(F∞). This allows further classification the type III factor and provides another construction of full type III1 factors having arbitrary Sd invariant of Connes. The free products considered in this paper are not limited to free products of finite dimensional algebras, but can be of a quite general form.