Lie algebras with ad-invariant metrics. A survey

TL;DR

This survey reviews Lie algebras with ad-invariant metrics, summarizing key concepts, constructions, and examples, to provide a comprehensive overview of the main research in this area.

Contribution

It compiles and synthesizes existing research on Lie algebras with ad-invariant metrics, highlighting main features and providing low-dimensional examples.

Findings

Summarizes key notions and constructions.

Provides examples in low dimensions.

Highlights main research directions.

Abstract

This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low dimensions.