Loading Web-Font TeX/Main/Regular
| Register
\newcommand{\Cat}{{\rm Cat}} \newcommand{\A}{\mathcal A} \newcommand{\freestar}{ \framebox[7pt]{$\star$} }

4. C^* Algebras

    1. C^* Super-Rigidity for Non-Discrete Groups Acting on Trees


      Add remark

      Problem 4.1.

      [S. Raum] Does C^*_r(G_1)\cong C^*_r(G_2) imply that G_1\cong G_2 ?
        1. Remark. [Sven Raum] A more instance of this problem is: can the finite permutation group F be recovered from the reduced group C*-algebra of a Burger-Moses group U(F)?


            • Add remark

              Problem 4.2.

              [S. Raum] Find torsion-free simple groups such that \Gamma_1\not\cong \Gamma_2 and C^*_r(\Gamma_1)\cong C^*_r(\Gamma_2) .


                • Add remark

                  Problem 4.3.

                  Is C^*_r(\mathbb{F}_\infty) finitely generated?


                    • Add remark

                      Problem 4.4.

                      [S. Raum] Is \left(\mathbb{Z}/2\mathbb{Z} \right)^{(\mathbb{F}_2)}\rtimes (\mathbb{F}_2\times\mathbb{F}_2) C^* super-rigid?
                        1. Remark. [S. Raum] While the resulting C^* algebra does not have a unique trace, all traces can be described.


                            • Add remark

                              Problem 4.5.

                              [S. Vaes] Prove cocycle superrigidity for Bernoulli actions of property (T) groups with totally disconnected target groups.

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