Rigidity for von Neumann algebras and their invariants
By S. Vaes. 2010
104 citations recorded by the source corpus.
We give a survey of recent classification results for crossed product von Neumann algebras arising from measure preserving group actions on probability spaces. This includes II_1 factors with uncountable fundamental groups and the construction of W*-superrigid actions where the crossed product entirely remembers the initial group action that it was constructed from.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c97541ab47e2bad52e56151e5423cec06eedb85a
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In Algebra and Number Theory
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In Mathematical Physics
Citations in the corpus
- Orbit Equivalence and Measured Group Theory (2010, methodology): “This is very much connected from its birth with operator algebras [MvN36]; many of the recent progresses in both areas were made conjointly (see [Pop07b, Vae07, Vae10]).”
- A random matrix approach to the Peterson-Thom conjecture (2020, unknown): “See [64, 67, 68, 38, 39] for further results, including resolutions”
- Cartan subalgebras of amalgamated free product II$_1$ factors (2012, result): “nsidered intractable. During the last decade, S. Popa’s deformation/rigidity theory has led to spectacular progress in the classification of group measure space II1 factors (see the surveys [Po07] and [Va10a]). This was in part made possible by several results providing classes of group measure space”
- Continuous orbit equivalence rigidity (2015, background): “Here is a classical result (see [11, 31, 32] for more details).”