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Some applications of
group-theoretic Rips constructions to the classification of
von Neumann algebras
Ionuţ Chifan, Sayan Das and Krishnendu Khan |
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Vol. 16 (2023), No. 2, 433–476
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Abstract |
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We study various von Neumann algebraic rigidity aspects for the property (T) groups that arise via the Rips construction developed by Belegradek and Osin (Groups Geom. Dyn. 2:1 (2008), 1–12) in geometric group theory. Specifically, developing a new interplay between Popa’s deformation/rigidity theory (Int. Congr. Math, I (2007), 445–477) and geometric group theory methods, we show that several algebraic features of these groups are completely recognizable from the von Neumann algebraic structure. In particular, we obtain new infinite families of pairwise nonisomorphic property (T) group factors, thereby providing positive evidence towards Connes’ rigidity conjecture. In addition, we use the Rips construction to build examples of property (T) II-factors which possess maximal von Neumann subalgebras without property (T), which answers a question raised by Y. Jiang and A. Skalski (arXiv:1903.08190 (2019), version 3). |
Mathematical Subject Classification
Primary: 20F06, 46L36
Secondary: 20F65, 20F67
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Milestones
Received: 2 June 2020
Revised: 8 July 2021
Accepted: 11 August 2021
Published: 3 May 2023
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Authors |
| Ionuţ Chifan | |
| Department of Mathematics The University of Iowa Iowa City, IA United States |
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| Sayan Das | |
| Department of Mathematics University of California Riverside Riverside, CA United States |
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| Krishnendu Khan | |
| Department of Mathematics The University of Iowa Iowa City, IA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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