Relative solidity for biexact groups in measure equivalence

Fuente: arXiv
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Main Authors: Ding, Changying, Drimbe, Daniel
Format: Preprint
Published: 2025
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author Ding, Changying
Drimbe, Daniel
author_facet Ding, Changying
Drimbe, Daniel
contents We demonstrate a relative solidity property for the product of a nonamenable biexact group with an arbitrary infinite group in the measure equivalence setting. Among other applications, we obtain the following unique product decomposition for products of nonamenable biexact groups, strengthening \cite{Sa09}: for any nonamenable biexact groups $Γ_1,\cdots, Γ_n$, if a product group $Λ_1\times Λ_2$ is measure equivalent to $\times_{k=1}^nΓ_k$, then there exists a partition $T_1\sqcup T_2=\{1,\dots, n\}$ such that $Λ_i$ is measure equivalent to $\times_{k\in T_i}Γ_k$ for $i=1,2$.
format Preprint
id arxiv_https___arxiv_org_abs_2503_24167
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Relative solidity for biexact groups in measure equivalence
Ding, Changying
Drimbe, Daniel
Operator Algebras
Group Theory
We demonstrate a relative solidity property for the product of a nonamenable biexact group with an arbitrary infinite group in the measure equivalence setting. Among other applications, we obtain the following unique product decomposition for products of nonamenable biexact groups, strengthening \cite{Sa09}: for any nonamenable biexact groups $Γ_1,\cdots, Γ_n$, if a product group $Λ_1\times Λ_2$ is measure equivalent to $\times_{k=1}^nΓ_k$, then there exists a partition $T_1\sqcup T_2=\{1,\dots, n\}$ such that $Λ_i$ is measure equivalent to $\times_{k\in T_i}Γ_k$ for $i=1,2$.
title Relative solidity for biexact groups in measure equivalence
topic Operator Algebras
Group Theory
url https://arxiv.org/abs/2503.24167