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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].
|Journal||Bulletin of the Belgian Mathematical Society - Simon Stevin|
|Publication status||Published - Dec 2022|
- Thompson's group F
- infinite trees
- equivariant compactification
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- 1 Active
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
Project: Research Councils