Posetted trees and Baker-Campbell-Hausdorff product

TL;DR

This paper introduces posetted trees as a combinatorial tool to derive an explicit expression for the Baker-Campbell-Hausdorff formula, enhancing understanding of Lie algebra exponentials.

Contribution

It presents a novel combinatorial approach using posetted trees to explicitly formulate the Baker-Campbell-Hausdorff product.

Findings

Explicit formula for BCH using posetted trees

New combinatorial framework for Lie algebra calculations

Simplifies understanding of exponential maps in Lie theory

Abstract

We introduce the combinatorial notion of posetted trees and we use it in order to write an explicit expression of the Baker-Campbell-Hausdorff formula.