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

Research output: Contribution to journal › Journal article › Research › 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].

Original language	English
Journal	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	29
Issue number	3
Pages (from-to)	359-370
ISSN	1370-1444
DOIs	https://doi.org/10.36045/j.bbms.211208
Publication status	Published - Dec 2022

Keywords

Thompson's group F
infinite trees
equivariant compactification
Thompson’s group F

Documents & Links

10.36045/j.bbms.211208

https://arxiv.org/pdf/2303.10363

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1 Finished

Independent Research Fund Denmark - Automorphisms and Invariants of Operator Algebras
Kyed, D. (Co-PI), Szymanski, W. (PI), Kaad, J. (Co-PI), Eilers, S. (Co-PI), Törnquist, A. (Co-PI), Nest, R. (Co-PI), Thomsen, K. (Co-PI) & Thorbjørnsen, S. (Co-PI)
01/09/2017 → 01/09/2024
Project: Research Councils

Cite this

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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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AU - Szymanski, Wojciech

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N2 - 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].

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

U2 - 10.36045/j.bbms.211208

DO - 10.36045/j.bbms.211208

M3 - Journal article

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VL - 29

SP - 359

EP - 370

JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

IS - 3

ER -

The action of the Thompson group F on infinite trees

Abstract

Keywords

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Independent Research Fund Denmark - Automorphisms and Invariants of Operator Algebras

Cite this