# Pseudo Maurer-Cartan perturbation algebra and pseudo perturbation lemma

## TL;DR

This paper introduces a new algebraic structure called the pseudo Maurer-Cartan perturbation algebra, proves a key structural result, and derives a pseudo perturbation lemma that generalizes the classical perturbation lemma.

## Contribution

It presents a novel algebraic framework and a generalized perturbation lemma, extending the classical results in algebraic perturbation theory.

## Key findings

- Established the pseudo Maurer-Cartan perturbation algebra
- Proved a structural theorem for this algebra
- Derived the pseudo perturbation lemma, implying the classical perturbation lemma

## Abstract

We introduce the pseudo Maurer-Cartan perturbation algebra, establish a structural result and explore the structure of this algebra. That structural result entails, as a consequence, what we refer to as the pseudo perturbation lemma. This lemma, in turn, implies the ordinary perturbation lemma.