Maximal Injective Subalgebras of Tensor Products of Free Groups Factors

2005/08/16 by Junhao Shen, Shen, Junhao
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.math/0508305

openalex publication_date 2005/08/16 · arxiv created 2005/08/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we proved the following results. Let L(F(n_i)) be the free group factor on n_i generators and λ(g_i) be one of standard generators of L(F(n_i)) for 1≤ i≤ N. Let \A_i be the abelian von Neumann subalgebra of L(F(n_i)) generated by λ(g_i). Then the abelian von Neumann subalgebra ⊗_i=1^N\A_i is a maximal injective von Neumann subalgebra of ⊗_i=1^N L(F(n_i)). When N is equal to infinity, we obtained McDuff factors that contain maximal injective abelian von Neumann subalgebras.

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