| Résume | Résumé : As the analogue of ergodic group theory, I will give a brief introduction to the noncommutative ergodic theory of W*-inclusions initiated by Das-Peterson, especially the Furstenberg entropy theory in both settings. Then I will present some results that bridge the group and von Neumann algebra settings, focusing on the main result: the rigidity of Furstenberg entropy under ucp maps and quasi-factor maps. For most of the results, the group case appeared first and inspired its counterparts in the von Neumann algebra setting. However, the main result presents a surprising example of the exact opposite. |
