Strongly singular MASA's and mixing actions in finite von Neumann algebras

2006/02/08 by Paul Jolissaint, Jolissaint, Paul, Stalder, Yves
Mathematics · #20E06 #46L10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.math/0602158

openalex publication_date 2006/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Γ be a countable group and let Γ₀ be an infinite abelian subgroup of Γ. We prove that if the pair (Γ,Γ₀) satisfies some combinatorial condition called (SS), then the abelian subalgebra A=L(Γ₀) is a singular MASA in M=L(Γ) which satisfies a weakly mixing condition. If moreover it satisfies a stronger condition called (ST), then it provides a singular MASA with a strictly stronger mixing property. We describe families of examples of both types coming from free products, HNN extentions and semidirect products, and in particular we exhibit examples of singular MASA's that satisfy the weak mixing condition but not the strong mixing one.

Related

• Mixing and weakly mixing abelian subalgebras of type II₁ factors
• Mixing subalgebras of finite von Neumann algebras
• Strongly Singular Masas in Type II₁ Factors
• Maximal injective and mixing masas in group factors
• The Laplacian subalgebra of the k-folded tensor product of the free group factor with itself is a strongly singular masa