Differential Invariants of SL(2) and SL(3)-ACTIONS on R^2

TL;DR

This paper computes differential invariants resulting from the prolonged actions of SL(2) and SL(3) groups on jet spaces of R^2, advancing the understanding of their symmetry properties.

Contribution

It introduces methods to calculate nth prolonged infinitesimal generators and differential invariants for SL(2) and SL(3) actions on R^2.

Findings

Explicit formulas for differential invariants of SL(2) and SL(3) actions.

Methodology for calculating nth prolonged infinitesimal generators.

Enhanced understanding of symmetry structures in jet spaces.

Abstract

The main purpose of this paper is calculation of differential invariants which arise from prolonged actions of two Lie groups SL(2) and SL(3) on the $n$th jet space of $R^2$. It is necessary to calculate $n$th prolonged infenitesimal generators of the action.