Masas and Bimodule Decompositions of \rmII₁ Factors

2008/12/06 by Kunal Mukherjee, Mukherjee, Kunal
Mathematics · Physics and Astronomy · #46Lxx #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0812.1257

openalex publication_date 2008/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The measure-multiplicity-invariant for masas in \rmII₁ factors was introduced in \citeMR2261688 to distinguish masas that have the same Pukánszky invariant. In this paper we study the measure class in the measure-multiplicity-invariant. This is equivalent to studying the standard Hilbert space as an associated bimodule. We characterize the type of any masa depending on the left-right-measure using Baire category methods (selection principle of Jankov and von Neumann). We present a second proof of Chifan's result on normalisers and a measure theoretic proof of the equivalence of weak asymptotic homomorphism property (WAHP) and singularity that appeared in \citeMR2417416.

Citations

• On the normalizing algebra of a MASA in a II₁ Factor
• On Groups of Measure Preserving Transformations. I

Related

• Singular Masas and Measure-Multiplicity Invariant
• Mixing and weakly mixing abelian subalgebras of type II₁ factors
• Coarse decomposition of II₁ factors
• Generator masas in q-deformed Araki-Woods von Neumann algebras and factoriality
• Unitary perturbations of masas in type II₁ factors