On Deformations of n-Lie algebras

TL;DR

This paper reviews the deformation theory of n-Lie algebras, including formal deformations, degenerations, and quantization, providing a generalized framework beyond traditional approaches.

Contribution

It introduces a generalized deformation approach using unital commutative associative algebras as bases for n-Lie algebra deformations.

Findings

Summarizes 1-parameter formal deformation theory for n-Lie algebras

Provides a generalized deformation framework with arbitrary base algebras

Discusses degenerations and quantization of n-Lie algebras

Abstract

The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and quantization of $n$-Lie algebras.