A free product pair rigidity result in von Neumann algebras
Yoshimichi Ueda
TL;DR
This paper demonstrates that the structure of free product pairs of certain von Neumann algebras uniquely encodes the number of components and their states, revealing a rigidity property.
Contribution
It establishes a new rigidity result for free product pairs of amenable type III$_1$ factors with weakly mixing states, showing they determine their components uniquely.
Findings
Free product pairs remember the number of components.
States on free product pairs are uniquely determined.
Rigidity holds for finitely many copies of the algebra.
Abstract
We prove that the free product pair of any finitely many copies of the unique amenable type III factor endowed with weakly mixing states remembers the number of free components and the given states.
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