Semidirect product rigidity of group von Neumann algebras arising from class \mathscrS, inductive limits and fundamental group

2022/02/09 by Sayan Das, Das, Sayan, Krishnendu Khan +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2202.04280

openalex publication_date 2022/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study property (T) groups arising from Rips construction in geometric group theory in the spirit of \citeCDK19 and certain inductive limit groups from this class. Using interplay between Popa's deformation/rigidity and methods in geometric group theory we are able to extend the class of groups considered in \citeCDK19 that remembers semidirect product features while passing to the group von Neumann algebras. Combining these results with the method developed in \citeCDHK20 we are able to produce more examples of property (T) group factors with trivial fundamental group. The inductive limit groups do not have property (T) and provides examples of more factors with trivial fundamental group. We are also able to show Cartan rigidity for these groups.

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