Fixed point subalgebras of Weil algebras: from geometric to algebraic questions

TL;DR

This paper surveys fixed point subalgebras of Weil algebras and their applications in differential geometry, focusing on classification problems related to bundles of generalized velocities and contact elements.

Contribution

It provides a comprehensive overview of fixed point subalgebras of Weil algebras and demonstrates several key claims relevant to differential geometry.

Findings

Identification of fixed point subalgebras in various Weil algebras

Application of these subalgebras to classification problems in differential geometry

Clarification of the structure of Weil algebras in geometric contexts

Abstract

The paper is a survey of some results about Weil algebras applicable in differential geometry, especially in some classification questions on bundles of generalized velocities and contact elements. Mainly, a number of claims concerning a form of fixed points subalgebras of various Weil algebra is demonstrated.