Affine actions on non-archimedean trees

الأصل · EN

We initiate the study of affine actions of groups on Λ-trees for a general ordered abelian group Λ; these are actions by dilations rather than isometries. This gives a common generalisation of isometric action on a Λ-tree, and affine action on an -tree as studied by I. Liousse. The duality between based length functions and actions on Λ-trees is generalised to this setting. We are led to consider a new class of groups: those that admit a free affine action on a Λ-tree for some Λ. Examples of such groups are presented, including soluble Baumslag-Solitar groups and the discrete Heisenberg group.