A type III$_1$ factor with the smallest outer automorphism group
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929507197255680 |
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| author | Chakraborty, Soham |
| author_facet | Chakraborty, Soham |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04702 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A type III$_1$ factor with the smallest outer automorphism group Chakraborty, Soham Operator Algebras 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. |
| title | A type III$_1$ factor with the smallest outer automorphism group |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2312.04702 |