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| Format: | Preprint |
| Published: |
2006
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0601188 |
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| _version_ | 1866908453052612608 |
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| author | Houdayer, Cyril |
| author_facet | Houdayer, Cyril |
| contents | We give in this paper a new construction of factors of type ${\rm III_1}$. Under certain assumptions, we can, thanks to a result by Popa, give a complete classification for this family of factors. Although these factors are never full, we can nevertheless, in many cases, compute Connes' $τ$ invariant. We obtain a new example of an uncountable family of pairwise non-isomorphic factors of type ${\rm III_1}$ with the same $τ$ invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0601188 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | A new construction of factors of type ${\rm III_1}$ Houdayer, Cyril Operator Algebras 46L10 We give in this paper a new construction of factors of type ${\rm III_1}$. Under certain assumptions, we can, thanks to a result by Popa, give a complete classification for this family of factors. Although these factors are never full, we can nevertheless, in many cases, compute Connes' $τ$ invariant. We obtain a new example of an uncountable family of pairwise non-isomorphic factors of type ${\rm III_1}$ with the same $τ$ invariant. |
| title | A new construction of factors of type ${\rm III_1}$ |
| topic | Operator Algebras 46L10 |
| url | https://arxiv.org/abs/math/0601188 |