# Calculation of L2-dimension

For a group $G$, can we calculate $dim^{(2)}_{\mathcal{N}G}(\ell^2 G)$, where $\mathcal{N}G$ is the von Neumann algebra of $G$ and $\ell^2 G$ is the Hilbert space on $G$? I want to see whether this is finite or not.

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