Cohomology and Deformations of $n$-Lie algebra morphisms

TL;DR

This paper develops cohomology theories and studies deformation properties of $n$-Lie algebra morphisms, motivated by applications in physics like Nambu Mechanics and String Theory.

Contribution

It introduces cohomology complexes for $n$-Lie algebra morphisms and analyzes their deformation theory, including infinitesimal deformations and obstructions.

Findings

Defined cohomology complexes for $n$-Lie algebra morphisms

Analyzed infinitesimal and equivalent deformations

Provided various illustrative examples

Abstract

The study of $n$-Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to define cohomology complexes and study deformation theory of $n$-Lie algebra morphisms. We discuss infinitesimal deformations, equivalent deformations and obstructions. Moreover, we provide various examples.