The action of the Thompson group F on infinite trees

Jeong Hee Hong; Wojciech Szymanski

doi:10.36045/j.bbms.211208

The action of the Thompson group F on infinite trees

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

Abstract

We construct an action of the Thompson group F on a compact space built from pairs of infinite, binary rooted trees. The action arises as an F-equivariant compactification of the action of F by translations on one of its homogeneous spaces, F/H_2, corresponding to a certain subgroup H_2 of F. The representation of F on the Hilbert space l^2(F/H_2) is faithful on the complex group algebra C[F].

Originalsprog	Engelsk
Tidsskrift	Bulletin of the Belgian Mathematical Society - Simon Stevin
Vol/bind	29
Udgave nummer	3
Sider (fra-til)	359-370
ISSN	1370-1444
DOI	https://doi.org/10.36045/j.bbms.211208
Status	Udgivet - dec. 2022

Dokumenter og links

10.36045/j.bbms.211208

https://arxiv.org/pdf/2303.10363

1 Igangværende

Independent Research Fund Denmark - Automorphisms and Invariants of Operator Algebras
Kyed, D., Szymanski, W., Kaad, J., Eilers, S., Törnquist, A., Nest, R., Thomsen, K. & Thorbjørnsen, S.
01/09/2017 → 01/09/2024
Projekter: Projekt › Danske forskningsråd

Citationsformater

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abstract = "We construct an action of the Thompson group F on a compact space built from pairs of infinite, binary rooted trees. The action arises as an F-equivariant compactification of the action of F by translations on one of its homogeneous spaces, F/H_2, corresponding to a certain subgroup H_2 of F. The representation of F on the Hilbert space l^2(F/H_2) is faithful on the complex group algebra C[F].",

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AB - We construct an action of the Thompson group F on a compact space built from pairs of infinite, binary rooted trees. The action arises as an F-equivariant compactification of the action of F by translations on one of its homogeneous spaces, F/H_2, corresponding to a certain subgroup H_2 of F. The representation of F on the Hilbert space l^2(F/H_2) is faithful on the complex group algebra C[F].

KW - Thompson's group F

KW - infinite trees

KW - equivariant compactification

KW - Thompson’s group F

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DO - 10.36045/j.bbms.211208

M3 - Journal article

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VL - 29

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JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

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The action of the Thompson group F on infinite trees

Abstract

Dokumenter og links

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Independent Research Fund Denmark - Automorphisms and Invariants of Operator Algebras

Citationsformater