Central sequences in the factor associated with Thompson’s group $F$

Jolissaint, Paul

Annales de l'Institut Fourier, Tome 48 (1998) no. 4, pp. 1093-1106.

Nous montrons que le facteur $L\left(F\right)$, de type ${\mathrm{II}}_1$ engendré par la représentation régulière de $F$, est isomorphe à son produit tensoriel avec le facteur hyperfini de type ${\mathrm{II}}_1$. Cela implique que le groupe unitaire de $L\left(F\right)$ est contractile par rapport à la topologie définie par la norme hilbertienne naturelle.

We prove that the type ${\mathrm{II}}_1$ factor $L\left(F\right)$ generated by the regular representation of $F$ is isomorphic to its tensor product with the hyperfinite type ${\mathrm{II}}_1$ factor. This implies that the unitary group of $L\left(F\right)$ is contractible with respect to the topology defined by the natural Hilbertian norm.

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