English

Some unique group-measure space decomposition results

Operator Algebras 2019-12-19 v2 Group Theory

Abstract

Using an approach emerging from the theory of closable derivations on von Neumann algebras, we exhibit a class of groups CR satisfying the following property: given any groups G_1, G_2 in CR, then any free, ergodic, measure preserving action on a probability space G_1 x G_2 on X gives rise to a von Neumann algebra with unique group measure space Cartan subalgebra. Pairing this result with Popa's Orbit Equivalence Superrigidity Theorem we obtain new examples of W*-superrigid actions.

Keywords

Cite

@article{arxiv.1010.5194,
  title  = {Some unique group-measure space decomposition results},
  author = {Ionut Chifan and Jesse Peterson},
  journal= {arXiv preprint arXiv:1010.5194},
  year   = {2019}
}

Comments

Revised proofs in Section 4

R2 v1 2026-06-21T16:33:51.021Z