Factors from trees

TL;DR

This paper constructs type  factors from group actions on homogeneous trees, providing a discrete analogue to a known continuous case involving hyperfinite factors and boundary actions.

Contribution

It introduces a method to build type  factors from group actions on trees, extending the theory of operator algebras in a new discrete setting.

Findings

Constructed factors of type  from group actions on trees.

Established a discrete analogue of Spatzier's boundary action result.

Connected group actions on trees to the structure of von Neumann algebras.

Abstract

We construct factors of type $\tn$ for $n\in\NN, n\geq 2$ from group actions on homogeneous trees and their boundaries. Our result is a discrete analogue of a result of R.J Spatzier, where the hyperfinite factor of type $\tone$ is constructed from a group action on the boundary of the universal cover of a manifold.