The noncommutative heat equation and certain Lie series

TL;DR

This paper investigates the convergence of Lie series expansions like Magnus and Wilcox using a non-commutative heat equation derived from the Maurer-Cartan equation, offering new insights into their mathematical properties.

Contribution

It introduces a novel approach connecting non-commutative heat equations with Lie series convergence analysis, which is a new perspective in the field.

Findings

Convergence criteria for Lie series expansions established.

Connection between Maurer-Cartan equation and heat equations demonstrated.

New theoretical framework for analyzing Lie series expansions.

Abstract

We approach the convergence of the Magnus, Wilcox, and symmetric Wilcox expansions by a non-commutative heat equation derived from the Maurer-Cartan equation.