A type 𝐼𝐼𝐼₁ factor with the smallest outer automorphism group

Chakraborty, Soham

doi:10.1090/tran/9324

A type $\mathrm {III}_{1}$ factor with the smallest outer automorphism group
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by Soham Chakraborty;

Trans. Amer. Math. Soc. 378 (2025), 1593-1617

DOI: https://doi.org/10.1090/tran/9324

Published electronically: October 25, 2024

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Abstract:

The canonical modular homomorphism provides an embedding of $\mathbb {R}$ into the outer automorphism group $Out(M)$ of any type $\mathrm {III}_{1}$ factor $M$. We provide an explicit construction of a full factor of type $\mathrm {III}_{1}$ 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 $\mathrm {III}_{1}$ factor by using an amalgamated free product construction.

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