# 3-Commutators Revisited

## TL;DR

This paper introduces new multi-commutator structures that generalize 3-commutators, applied to elliptic systems with anti-self-dual potentials, revealing compensation phenomena akin to those in anti-symmetric potential systems.

## Contribution

The paper develops a novel class of multi-commutator structures that extend previous 3-commutators, enabling analysis of elliptic systems with anti-self-dual potentials.

## Key findings

- Identification of new compensation phenomena in elliptic systems
- Generalization of 3-commutators to multi-commutator structures
- Application to pseudo-differential elliptic systems with anti-self-dual potentials

## Abstract

We present a class of Pseudo-differential elliptic systems with anti-self-dual potentials on ${\mathbb R}$ satisfying compensation phenomena similar to the ones for elliptic systems with anti-symmetric potentials. These compensation phenomena are based on new "multi-commutator" structures generalizing the 3-commtators introduced by the authors in a previous work some years ago.