Lie symmetries of a third order PDE system

TL;DR

This paper investigates the symmetry properties of a specific class of third order PDE systems related to CR-geometry, establishing an exact upper bound on their Lie symmetry algebra.

Contribution

It proves that such PDE systems have at most a ten-dimensional Lie symmetry algebra and confirms that this bound is sharp.

Findings

Maximum ten-dimensional Lie symmetry algebra for the PDE system.

The bound on symmetry algebra dimension is exact.

Provides insights into the symmetry structure of CR-geometry PDEs.

Abstract

In this paper we show that a third order PDE system that is a general form of a CR-geometry PDE system has at most a ten-dimensional Lie symmetry algebra. We also show that this estimate is precise.