Intersections of finite families of finite index subfactors

2004/06/16 by Vaughan F. R. Jones, Feng Xu, Jones, Vaughan F. R. +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.MP #math.OA

paper · pdf · doi:10.48550/arxiv.math/0406331

17 pages, to appear in International Journal of Mathematics

openalex publication_date 2004/06/16 · arxiv created 2004/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that finiteness of the index of the intersection of a finite set of finite index subalgebras in a von Neumann algebra (with small centre) is equivalent to the finite dimensionality of the algebra generated by the conditional expectations onto the subalgebras.

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