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arXiv · 2312.04702

A type III$_1$ factor with the smallest outer automorphism group

Soham Chakraborty
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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 III$_{1}$ factor $M$. We provide an explicit construction of a full factor of type III$_{1}$ with separable predual such that the outer automorphism group is minimal, i.e. this embedding is an isomorphism. We obtain such a III$_{1}$ factor by using an amalgamated free product construction.

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Soham Chakraborty. 2023-12-07. A type III$_1$ factor with the smallest outer automorphism group. https://arxiv.org/abs/2312.04702

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