A Modified Version of Free Orbit-Dimension of von Neumann Algebras

TL;DR

This paper introduces a new invariant for finite von Neumann algebras that extends the free orbit-dimension concept to non-separable cases, demonstrating its independence from generating sets and broadening previous results.

Contribution

It presents a modified free orbit-dimension invariant applicable to non-finitely generated von Neumann algebras, expanding the scope of prior work.

Findings

Invariant is independent of generating set

Extension of results to non-finitely generated algebras

Broader applicability of free orbit-dimension concept

Abstract

Based on the notion of free orbit-dimension introduced by D. Hadwin and J. Shen [4], we introduce a new invariant on finite von Neumann algebras that do not necessarily act on separable Hilbert space. We show that this invariant is independent on the generating set, and we extend some results in [4] to von Neumann algebras that are not finitely generated.