Mixing and weakly mixing abelian subalgebras of type II₁ factors

2016/12/30 by Cameron, Jan, Fang, Junsheng, Mukherjee, Kunal
#46L10 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1612.09569

Abstract

This paper studies weakly mixing (singular) and mixing masas in type \rmII₁ factors from a bimodule point of view. Several necessary and sufficient conditions to characterize the normalizing algebra of a masa are presented. We also study the structure of mixing inclusions, with special attention paid to masas of product class. A recent result of Jolissaint and Stalder concerning mixing masas arising out of inclusions of groups is revisited. One consequence of our structural results rules out the existence of certain Koopman-realizable measures, arising from semidirect products, which are absolutely continuous but not Lebesgue. We also show that there exist uncountably many pairwise non--conjugate mixing masas in the free group factors each with Pukánszky invariant \1,∞\.

Related

• Strongly singular MASA's and mixing actions in finite von Neumann algebras
• Maximal injective and mixing masas in group factors
• A class of \rm II₁ factors with an exotic abelian maximal amenable subalgebra
• Mixing subalgebras of finite von Neumann algebras
• Masas and Bimodule Decompositions of \rmII₁ Factors