On the cohomology of Lie algebras with an invariant inner product

TL;DR

This paper classifies low-dimensional metric Lie algebras over complex and real fields, introducing cyclic cohomology to analyze their metric deformations.

Contribution

It provides a comprehensive classification of metric Lie algebras up to dimension 6 and introduces cyclic cohomology as a tool for studying metric deformations.

Findings

Complete classification of metric Lie algebras up to dimension 5 over  and .

Classification of metric Lie algebras over  in dimension 6.

Introduction of cyclic and reduced cyclic cohomology for deformation analysis.

Abstract

In this work we consider all metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over \C and \R up to dimension 5 and all metric Lie algebras over \C in dimension 6. We introduce cyclic and reduced cyclic cohomology to identify their metric deformations.