Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable

TL;DR

This paper develops a formal method to compute infinitesimals for group actions on multispace of curves, extending Olver's moving frames approach to a more general setting.

Contribution

It introduces a recursion relation for infinitesimals in multispace, generalizing known prolongation relations from jet space to multispace.

Findings

Derived a recursion relation for infinitesimals in multispace

Extended Olver's moving frames approach to multispace

Provided a formal framework for group action analysis on curves

Abstract

This paper expands upon the work of Peter Olver's paper [Appl. Algebra Engrg. Comm. Comput. 11 (2001), 417-436], wherein Olver uses a moving frames approach to examine the action of a group on a curve within a generalization of jet space known as multispace. Here we seek to further study group actions on the multispace of curves by computing the infinitesimals for a given action. For the most part, we proceed formally, and produce in the multispace a recursion relation that closely mimics the previously known prolongation recursion relations for infinitesimals of a group action on jet space.