An Overview of Hopf Algebras of Trees and Their Actions on Functions

TL;DR

This paper provides an overview of various Hopf algebras constructed from different types of trees and explores their actions on function algebras, offering insights into their structures and applications.

Contribution

It systematically describes multiple Hopf algebras based on trees and details their actions on functions, expanding understanding of their algebraic and combinatorial properties.

Findings

Classification of Hopf algebras from trees and labeled trees

Descriptions of actions on algebra of functions

Connections between tree structures and algebraic operations

Abstract

We provide an expository account of some of the Hopf algebras that can be defined using trees, labeled trees, ordered trees and heap ordered trees. We also describe some actions of these Hopf algebras on algebra of functions.