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3. Structural Properties of von Neumann Algebras

    1. McDuff

      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?
        • Problem 3.2.

          [S. Popa] If $\beta_1^{(2)}(\Gamma)\neq 0 $, then does it follow that $\Gamma $ is Cartan rigid.
            • 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 $L(K\backslash G / K)$
                • 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) $.
                    • Problem 3.5.

                      [org.aimpl.user:rdesantiago@math.ucla.edu] 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.