On the Laplacian subalgebra of certain tensors of group von Neumann algebras

2005/10/11 by Teodor Ştefan Bîldea, Bildea, Teodor Stefan
Mathematics · Physics and Astronomy · #20E05 #46L10 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.math/0510209

openalex publication_date 2005/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we exhibit strongly singular maximal abelian subalgebras living inside certain k-folded tensors of von Neumann group factors. The two classes of groups under consideration are the free groups of rank greater than 2 and the free product of m>2 groups, all finite and having the same order p>2 (m>p-1). We prove actually more, namely that the unique trace preserving conditional expectations from these group factors onto their Laplacian subalgebras are asymptotic homomorphisms, which in turn implies that the subalgebras are strongly singular masas.

Related

• The Laplacian subalgebra of the k-folded tensor product of the free group factor with itself is a strongly singular masa
• The Laplacian Masa in a Free Group Factor
• Strongly Singular Masas in Type II₁ Factors
• Maximal Injective Subalgebras of Tensor Products of Free Groups Factors
• Strongly singular MASA's and mixing actions in finite von Neumann algebras