The Universal Post-Lie-Rinehart Algebra of Planar Aromatic Trees

TL;DR

This paper introduces the algebraic structure of tracial post-Lie-Rinehart algebras, generalizing existing algebraic frameworks, and describes the free object within this new category, expanding the theoretical landscape.

Contribution

It defines the structure of tracial post-Lie-Rinehart algebras and characterizes the free object in this algebraic category, extending prior algebraic theories.

Findings

Defined the algebraic structure of tracial post-Lie-Rinehart algebras

Described the free object in this algebraic category

Generalized pre-Lie-Rinehart and post-Lie algebroids

Abstract

This paper defines the algebraic structure of tracial post-Lie-Rinehart algebras and describes the free object in this category. Post-Lie-Rinehart algebras is a generalisation of pre-Lie-Rinehart algebras, and of post-Lie algebroids.