Groups of hierarchomorphisms of trees and related Hilbert spaces
Representation Theory
2013-01-16 v1 Functional Analysis
Group Theory
Abstract
Consider an infinite tree. A hierarchomorphism (spheromorphism) is a homeomorphism of the absolute which can be extended to the tree except a finite subtree. Examples of groups of hierarchomorphisms: groups of locally analitic diffeomorphisms of -adic line; also Richard Thompson groups. The groups of hierarchomorphisms have some properties similar to the group of diffeomorphisms of the circle. We discuss actions of groups of ierarchomorphisms in some natural Hilbert spaces associated with trees.
Cite
@article{arxiv.math/0106243,
title = {Groups of hierarchomorphisms of trees and related Hilbert spaces},
author = {Yurii A. Neretin},
journal= {arXiv preprint arXiv:math/0106243},
year = {2013}
}
Comments
22 pages, two pictures