C*-IRREDUCIBILITY OF COMMENSURATED SUBGROUPS

Li K, Scarparo E (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Pacific Journal of Mathematics

Book Volume: 322

Pages Range: 369-380

Journal Issue: 2

DOI: 10.2140/pjm.2023.322.369

Abstract

Given a commensurated subgroup Λ of a group Γ, we completely characterize when the inclusion Λ ≤ Γ is C*-irreducible and provide new examples of such inclusions. In particular, we obtain that PSL(n, ℤ) ≤ PGL(n,ℚ) is C*-irreducible for any n ∈ ℕ, and that the inclusion of a C*-simple group into its abstract commensurator is C*-irreducible. The main ingredient that we use is the fact that the action of a commensurated subgroup Λ ≤ Γ on its Furstenberg boundary ∂FΛ can be extended in a unique way to an action of Γ on ∂FΛ. Finally, we also investigate the counterpart of this extension result for the universal minimal proximal space of a group.

Authors with CRIS profile

Kang Li Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

Federal University of Pelotas / Universidade Federal de Pelotas (UFPEL) BR Brazil (BR)

How to cite

APA:

Li, K., & Scarparo, E. (2023). C*-IRREDUCIBILITY OF COMMENSURATED SUBGROUPS. Pacific Journal of Mathematics, 322(2), 369-380. https://dx.doi.org/10.2140/pjm.2023.322.369

MLA:

Li, Kang, and Eduardo Scarparo. "C*-IRREDUCIBILITY OF COMMENSURATED SUBGROUPS." Pacific Journal of Mathematics 322.2 (2023): 369-380.

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