The regular representation of Neretin groups is factorial

2025/06/30 by Morando, Basile · 4 citations
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2506.24029

Abstract

We show that the left regular representation of Neretin groups is factorial, providing the first example of a non-discrete simple group with this property. This is based on a new criterion of factoriality for totally disconnected groups. For groups G satisfying the criterion, we determine the type of the factor L(G) and derive factoriality results for crossed products associated to G-actions on von Neumann algebras.

Citations

• Almost unimodular groups
• Locally compact piecewise full groups of homeomorphisms
• Factoriality of twisted locally compact group von Neumann algebras
• C*-simplicity of relative profinite completions of generalized Baumslag-Solitar groups
• Piecewise strongly proximal actions, free boundaries and the Neretin groups
• Unitary representations of groups, duals, and characters
• Coloured Neretin Groups
• Locally compact groups acting on trees, the type I conjecture and\n non-amenable von Neumann algebras
• C*-simplicity of locally compact Powers groups
• Compact presentability of tree almost automorphism groups
• Generalised Hecke algebras and C^*-completions

Cited by

• On modular invariants of twisted group von Neumann algebras of almost unimodular groups
• On ergodicity of linear actions on ℝⁿ and factoriality of group von Neumann algebras
• Non-strong ergodicity of canonical actions of the Thompson groups
• Projective representations of almost unimodular groups

Related

• Piecewise strongly proximal actions, free boundaries and the Neretin groups
• On ergodicity of linear actions on ℝⁿ and factoriality of group von Neumann algebras
• Neretin groups admit no non-trivial invariant random subgroups
• Factoriality of twisted locally compact group von Neumann algebras
• Structure of \rm II₁ factors arising from free Bogoljubov actions of arbitrary groups