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

Soham Chakraborty

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

Operator Algebras 2024-09-23 v2

Authors: Soham Chakraborty

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.

Keywords

automorphism groups

Cite

@article{arxiv.2312.04702,
  title  = {A type III$_1$ factor with the smallest outer automorphism group},
  author = {Soham Chakraborty},
  journal= {arXiv preprint arXiv:2312.04702},
  year   = {2024}
}

Comments

v2: 34 pages, minor changes, added Section 2.3 (preliminaries). To appear in Trans. Amer. Math. Soc

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