december 2022 The Action of the Thompson Group $F$ on Infinite Trees
Jeong Hee Hong, Wojciech Szymański
Bull. Belg. Math. Soc. Simon Stevin 29(3): 359-370 (december 2022). DOI: 10.36045/j.bbms.211208

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 $\ell^2(F/H_2)$ is faithful on the complex group algebra $\mathbb{C}[F]$.

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Jeong Hee Hong. Wojciech Szymański. "The Action of the Thompson Group $F$ on Infinite Trees." Bull. Belg. Math. Soc. Simon Stevin 29 (3) 359 - 370, december 2022. https://doi.org/10.36045/j.bbms.211208

Information

Published: december 2022
First available in Project Euclid: 22 March 2023

Digital Object Identifier: 10.36045/j.bbms.211208

Subjects:
Primary: 20F65 , 22D25

Keywords: equivariant compactification , infinite trees , Thompson's group $F$

Rights: Copyright © 2022 The Belgian Mathematical Society

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Vol.29 • No. 3 • december 2022
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