Maximal injective and mixing masas in group factors

2010/04/01 by Paul Jolissaint, Jolissaint, Paul
Mathematics · #20E06 (Secondary) #46L10 (Primary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Operator Algebras (math.OA) #math.OA #msc:20E06 #msc:46L10

paper · pdf · doi:10.48550/arxiv.1004.0128

11 pages; misprints corrected

openalex publication_date 2010/04/01 · arxiv created 2010/08/04 · arxiv updated 2010/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present families of pairs of finite von Neumann algebras A⊂ M where A is a maximal injective masa in the type II₁ factor M with separable predual. Our results make use of the strong mixing and the asymptotic orthogonality properties of A in M and are borrowed from ideas of S. Popa who proved that if G is a non abelian free group and if a is one of its generators, then the von Neumann algebra generated by a is maximal injective in the factor L(G). Our results apply to pairs H<G where H is an infinite abelian subgroup of a suitable amalgamated product group G.

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