Subalgebras, subgroups, and singularity

Tattwamasi Amrutam; Yair Hartman

doi:https://doi.org/10.1112/blms.12939

Subalgebras, subgroups, and singularity

Tattwamasi Amrutam, Yair Hartman

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is concerned with the noncommutative analog of the normal subgroup theorem for certain groups. Inspired by Kalantar and Panagopoulos (arXiv:2108.02928, 2021, 16), we show that all (Formula presented.) -invariant subalgebras of (Formula presented.) and (Formula presented.) are ((Formula presented.) -)coamenable. The groups we work with satisfy a singularity phenomenon described by Bader et al. (Invent. Math. 229 (2022), 929–985). The setup of singularity allows us to obtain a description of (Formula presented.) -invariant intermediate von Neumann subalgebras (Formula presented.) in terms of the normal subgroups of (Formula presented.).

Original language	American English
Pages (from-to)	380-395
Number of pages	16
Journal	Bulletin of the London Mathematical Society
Volume	56
Issue number	1
DOIs	https://doi.org/10.1112/blms.12939
State	Published - 1 Jan 2024

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Subalgebras, subgroups, and singularity",

abstract = "This paper is concerned with the noncommutative analog of the normal subgroup theorem for certain groups. Inspired by Kalantar and Panagopoulos (arXiv:2108.02928, 2021, 16), we show that all (Formula presented.) -invariant subalgebras of (Formula presented.) and (Formula presented.) are ((Formula presented.) -)coamenable. The groups we work with satisfy a singularity phenomenon described by Bader et al. (Invent. Math. 229 (2022), 929–985). The setup of singularity allows us to obtain a description of (Formula presented.) -invariant intermediate von Neumann subalgebras (Formula presented.) in terms of the normal subgroups of (Formula presented.).",

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AB - This paper is concerned with the noncommutative analog of the normal subgroup theorem for certain groups. Inspired by Kalantar and Panagopoulos (arXiv:2108.02928, 2021, 16), we show that all (Formula presented.) -invariant subalgebras of (Formula presented.) and (Formula presented.) are ((Formula presented.) -)coamenable. The groups we work with satisfy a singularity phenomenon described by Bader et al. (Invent. Math. 229 (2022), 929–985). The setup of singularity allows us to obtain a description of (Formula presented.) -invariant intermediate von Neumann subalgebras (Formula presented.) in terms of the normal subgroups of (Formula presented.).

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Subalgebras, subgroups, and singularity

Abstract

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