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3. Structural Properties of von Neumann Algebras

    1. McDuff


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      Problem 3.1.

      [C. Houdayer] Assume that M\cong P_1\bar\otimes P_2 is McDuff. Does it follow that P_1 or P_2 is McDuff?


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          Problem 3.2.

          [S. Popa] If \beta_1^{(2)}(\Gamma)\neq 0 , then does it follow that \Gamma is Cartan rigid.


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              Problem 3.3.

              [S. Raum] Let G is a totally disconnected group and K\subseteq G compact.
              1. When do the K invariant vectors in L^2(K\backslash G) \subset L^2(G) generate L^2(G) .
              2. Describe criteria for the factoriality of L(K\backslash G / K)


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                  Problem 3.4.

                  [S. Vaes]
                  1. Find two trace-scaling automorphisms of L(\mathbb{F}_\infty)\bar\otimes \mathbb{B}(\ell^2) that are not outer conjugate.
                  2. Find two non-isomorphic type III_\lambda factors with discrete core L(\mathbb{F}_\infty)\bar\otimes \mathbb{B}(\ell^2) .


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                      Problem 3.5.

                      [Rolando de Santiago] Classify Cartan subalgebras of a II_1 factor M when M does not have a unique Cartan.

                          Cite this as: AimPL: Classification of group von Neumann algebras, available at http://aimpl.org/groupvonneumann.