Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states

Details Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states

1996-01-23

arxiv.org/abs/funct-an/9601003v1

Mathematics

Operator Algebras

46 pages. To appear in a volume of Fields Institute Communications edited by D.V. Voiculescu. This .tex file uses a .sty file

Scientific paper

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 $L(\freeF_\infty)$. This allows further classification the type~III factor and provides another construction of full type~III$_1$ 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.

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