We establish several classification results for compact extensions of tracial W∗-dynamical systems and for relatively independent joinings thereof for actions of arbitrary discrete groups. We use these results to answer a question of Austin, Eisner, and Tao and some questions raised by Duvenhage and King. Moreover, combining our results with an earlier classification of weakly mixing extensions by Popa, we can derive non-commutative Furstenberg–Zimmer type dichotomies on the L2-level. Although in general an adequate generalization of the Furstenberg–Zimmer tower of intermediate compact extensions does not seem possible in the von Neumann algebraic framework, we show that there always exists a non-commutative analogue of the finer Host–Kra–Ziegler tower for any ergodic action of a countable abelian group.
1
Dresden University of Technology (TUD), Germany
2
University of Copenhagen, Denmark
Asgar Jamneshan; Pieter Spaas. On compact extensions of tracial $W^{*}$-dynamical systems. Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 913-955. doi: 10.4171/ggd/801
@article{10_4171_ggd_801,
author = {Asgar Jamneshan and Pieter Spaas},
title = {On compact extensions of tracial $W^{*}$-dynamical systems},
journal = {Groups, geometry, and dynamics},
pages = {913--955},
year = {2025},
volume = {19},
number = {3},
doi = {10.4171/ggd/801},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/801/}
}
TY - JOUR
AU - Asgar Jamneshan
AU - Pieter Spaas
TI - On compact extensions of tracial $W^{*}$-dynamical systems
JO - Groups, geometry, and dynamics
PY - 2025
SP - 913
EP - 955
VL - 19
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/801/
DO - 10.4171/ggd/801
ID - 10_4171_ggd_801
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%R 10.4171/ggd/801
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