@article{3346c7ebfb784ac9873106b0c147bada,
title = "On invariant von Neumann subalgebras rigidity property",
abstract = "We say that a countable discrete group Γ satisfies the invariant von Neumann subalgebras rigidity (ISR) property if every Γ- invariant von Neumann subalgebra M in L(Γ) is of the form L(Λ) for some normal subgroup Λ◁Γ. We show many “negatively curved” groups, including all torsion free non-amenable hyperbolic groups and torsion free groups with positive first L2-Betti number under a mild assumption, and certain finite direct product of them have this property. We also discuss whether the torsion-free assumption can be relaxed.",
keywords = "First L-Betti number, Hyperbolic groups, Invariant von Neumann subalgebras",
author = "Tattwamasi Amrutam and Yongle Jiang",
note = "Funding Information: The first named author's research is supported by the Israel Science Foundation (Grant No. 1175/18). The second named author is supported by “the Fundamental Research Funds for the Central Universities” (Grant No. DUT19RC(3)075). The authors express their gratitude towards Adam Skalski for taking the time to read a near complete draft of this paper and for his numerous comments and suggestions which improved the exposition of this paper greatly. The authors also thank Adam Dor-On and Jesse Peterson for their helpful suggestions. The first named author is grateful near Mehrdad Kalantar and Yair Hartman for many helpful discussions regarding the problem. The first named author would also like to thank the officials (especially Kavita Ma'am) in the Israel Embassy, New Delhi. He was able to travel and start his postdoc position due to their timely help and intervention. We also thank the anonymous referee for his/her insightful comments and suggestions and for pointing out Remark 2.6, Lemma 2.8, and Proposition 3.1. Funding Information: The first named author's research is supported by the Israel Science Foundation (Grant No. 1175/18 ). The second named author is supported by “the Fundamental Research Funds for the Central Universities ” (Grant No. DUT19RC(3)075 ). The authors express their gratitude towards Adam Skalski for taking the time to read a near complete draft of this paper and for his numerous comments and suggestions which improved the exposition of this paper greatly. The authors also thank Adam Dor-On and Jesse Peterson for their helpful suggestions. The first named author is grateful near Mehrdad Kalantar and Yair Hartman for many helpful discussions regarding the problem. The first named author would also like to thank the officials (especially Kavita Ma'am) in the Israel Embassy, New Delhi. He was able to travel and start his postdoc position due to their timely help and intervention. We also thank the anonymous referee for his/her insightful comments and suggestions and for pointing out Remark 2.6 , Lemma 2.8 , and Proposition 3.1 . Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",
year = "2023",
month = mar,
day = "1",
doi = "10.1016/j.jfa.2022.109804",
language = "English",
volume = "284",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "5",
}