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

1996/01/23 by Kenneth J. Dykema, Dykema, Kenneth J.
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.funct-an/9601003

openalex publication_date 1996/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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_∞). 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.

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