A type III₁ factor with the smallest outer automorphism group

The canonical modular homomorphism provides an embedding of R R into the outer automorphism group O u t ( M ) Out(M) of any type I I I 1 III₁ factor M M . We provide an explicit construction of a full factor of type I I I 1 III₁ with separable predual such that the outer automorphism group is minimal, i.e. this embedding is an isomorphism and a homeomorphism. We obtain such a I I I 1 III₁ factor by using an amalgamated free product construction.