On ergodicity of linear actions on ℝⁿ and factoriality of group von Neumann algebras

2025/10/27 by Soham Chakraborty, Chakraborty, Soham, Chinmay Tamhankar +1
#math.OA #math.DS

paper · pdf · doi:10.48550/arxiv.2510.23864

Abstract

We give some natural conditions on actions of discrete countable groups on abelian locally compact groups of Lie type that imply factoriality of the group von Neumann algebras of their semidirect products. This allows us to give a fairly large class of examples of locally compact groups whose group von Neumann algebras are factors.

Citations

• The regular representation of Neretin groups is factorial
• Analysis of the Plancherel weight and factoriality of the group von Neumann algebras of non-unimodular almost unimodular groups
• Almost unimodular groups
• Factoriality of twisted locally compact group von Neumann algebras
• Factoriality of groupoid von Neumann algebras
• Unitary representations of groups, duals, and characters
• C*-simplicity of locally compact Powers groups
• Weak mixing properties for nonsingular actions
• On dense free subgroups of Lie groups

Related

• On fullness of von Neumann algebras associated with non-singular Borel\n equivalence relations
• Classification of actions of compact abelian groups on subfactors with index less than 4
• Factorization and boundedness for representations of locally compact groups on topological vector spaces
• Dynamical McDuff-type properties for group actions on von Neumann algebras
• Properly proximal groups and their von Neumann algebras