Symmetry Reduction of sh-Lie Structures and of Local Functionals

TL;DR

This paper explores how symmetry reduction techniques can be applied to sh-Lie structures and local functionals, especially when the Lie group action is transversal to the fibers of a vector bundle, expanding the understanding of symmetry reduction in geometric structures.

Contribution

It introduces a novel approach to reducing sh-Lie structures and local functionals using symmetry reduction with transversal Lie group actions.

Findings

Reduced sh-Lie structures via transversal symmetry actions

Method for reducing local functionals using symmetry ideas

Extension of symmetry reduction techniques to new geometric contexts

Abstract

Reduced sh-Lie structures have been studied for the case when a Lie group acts on the fibers of a vector bundle while preserving the base space of the bundle. In this paper we investigate how one obtains a reduced sh-Lie structure using the ideas of symmetry reduction where the action of the Lie group is transversal to the fibers of the bundle. We also show how local functionals are reduced using these ideas.