TY - JOUR
T1 - SOME APPLICATIONS OF GROUP-THEORETIC RIPS CONSTRUCTIONS TO THE CLASSIFICATION OF VON NEUMANN ALGEBRAS
AU - Chifan, Ionut
AU - Das, Sayan
AU - Khan, Krishnendu
N1 - Publisher Copyright:
© 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.
PY - 2023
Y1 - 2023
N2 - 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) II1-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).
AB - 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) II1-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).
UR - https://www.scopus.com/pages/publications/85159182289
U2 - 10.2140/apde.2023.16.433
DO - 10.2140/apde.2023.16.433
M3 - 文章
AN - SCOPUS:85159182289
SN - 2157-5045
VL - 16
SP - 433-l476
JO - Analysis and PDE
JF - Analysis and PDE
IS - 2
ER -