Cohomology and L2L2-Betti numbers for subfactors and quasi-regular inclusions
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Description: |
Shlyakhtenko, D (University of California, Los Angeles)
Wednesday 25th January 2017 - 11:30 to 12:30 |
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Created: | 2017-02-08 15:53 |
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Collection: | Operator algebras: subfactors and their applications |
Publisher: | Isaac Newton Institute |
Copyright: | Shlyakhtenko, D |
Language: | eng (English) |
Abstract: | Co-authors: Sorin Popa (UCLA) and Stefaan Vaes (Leuven)
We introduce L22-Betti numbers, as well as a general homology and cohomology theory for the standard invariants of subfactors, through the associated quasi-regular symmetric enveloping inclusion of II11 factors. We actually develop a (co)homology theory for arbitrary quasi-regular inclusions of von Neumann algebras. For crossed products by countable groups Γ, we recover the ordinary (co)homology of Γ. For Cartan subalgebras, we recover Gaboriau's L22-Betti numbers for the associated equivalence relation. In this common framework, we prove that the L22-Betti numbers vanish for amenable inclusions and we give cohomological characterizations of property (T), the Haagerup property and amenability. We compute the L22-Betti numbers for the standard invariants of the Temperley-Lieb-Jones subfactors and of the Fuss-Catalan subfactors, as well as for free products and tensor products. |
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