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We introduce the fundamental group $F(\mathcal{M})$ of a finite von Neumannalgebra $\mathcal{M}$ with finite dimensional normal trace space. The form of$F(\mathcal{M})$ is completely determined. Moreover, there exists a finite vonNeumann algebra $\mathcal{M}$ with finite dimensional normal trace space suchthat $F(\mathcal{M})=G$ for any conceivable groups $G$ as fundamental group.

Fundamental group of finite von Neumann algebras with finite dimensional normal trace space