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Based on the notion of free orbit-dimension of Hadwin-Shen (2007) we introduce a new invariant for finite von Neumann algebras with arbitrarily large generating sets and acting on Hilbert spaces of arbitrary dimension. We show that this invariant is independent of the generating set, and we extend results in Hadwin-Shen (2007) to this larger class of algebras.

A modified version of free orbit-dimension of von Neumann algebras