Groups of hierarchomorphisms of trees and related Hilbert spaces

Details Groups of hierarchomorphisms of trees and related Hilbert spaces Groups of hierarchomorphisms of trees and related Hilbert spaces

2001-06-28

arxiv.org/abs/math/0106243v1

Mathematics

Representation Theory

22 pages, two pictures

Scientific paper

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 $p$-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.

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