Strongly solid ${\rm II_1}$ factors with an exotic MASA
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2009
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| _version_ | 1866913943634575360 |
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| author | Houdayer, Cyril Shlyakhtenko, Dimitri |
| author_facet | Houdayer, Cyril Shlyakhtenko, Dimitri |
| contents | Using an extension of techniques of Ozawa and Popa, we give an example of a non-amenable strongly solid $\rm{II}_1$ factor $M$ containing an "exotic" maximal abelian subalgebra $A$: as an $A$,$A$-bimodule, $L^2(M)$ is neither coarse nor discrete. Thus we show that there exist $\rm{II}_1$ factors with such property but without Cartan subalgebras. It also follows from Voiculescu's free entropy results that $M$ is not an interpolated free group factor, yet it is strongly solid and has both the Haagerup property and the complete metric approximation property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0904_1225 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | Strongly solid ${\rm II_1}$ factors with an exotic MASA Houdayer, Cyril Shlyakhtenko, Dimitri Operator Algebras 46L10, 46L54 Using an extension of techniques of Ozawa and Popa, we give an example of a non-amenable strongly solid $\rm{II}_1$ factor $M$ containing an "exotic" maximal abelian subalgebra $A$: as an $A$,$A$-bimodule, $L^2(M)$ is neither coarse nor discrete. Thus we show that there exist $\rm{II}_1$ factors with such property but without Cartan subalgebras. It also follows from Voiculescu's free entropy results that $M$ is not an interpolated free group factor, yet it is strongly solid and has both the Haagerup property and the complete metric approximation property. |
| title | Strongly solid ${\rm II_1}$ factors with an exotic MASA |
| topic | Operator Algebras 46L10, 46L54 |
| url | https://arxiv.org/abs/0904.1225 |