Further results on monoids acting on trees

TL;DR

This paper advances the theory of semigroup actions on trees by refining the use of Lyndon-Chiswell length functions to construct and analyze elliptic actions, improving previous results.

Contribution

It introduces an improved method where the length function of the action matches the Lyndon-Chiswell length function, enhancing the understanding of semigroup actions on trees.

Findings

Constructed a tree T from the semigroup S using the length function.

Established that the length function of the action equals the Lyndon-Chiswell length function.

Extended previous results on semigroup actions on trees.

Abstract

This paper further develops the theory of arbitrary semigroups acting on trees via elliptic mappings. A key tool is the Lyndon-Chiswell length function L for the semigroup S which allows one to construct a tree T and an action of S on T via elliptic maps. Improving on previous results, the length function of the action will also be L.