Dictionary on Lie Superalgebras

TL;DR

This paper provides an accessible, dictionary-style overview of Lie superalgebras, covering their structure, representations, and supersymmetry, aimed at both beginners and experienced researchers.

Contribution

It offers a concise, easy-to-use reference on Lie superalgebras, summarizing key concepts and tools in a dictionary format for diverse audiences.

Findings

Clear definitions of Lie superalgebras and their properties

Summary of simple Lie superalgebras and their finite-dimensional representations

Introduction to supersymmetry concepts related to superalgebras

Abstract

The main definitions and properties of Lie superalgebras are proposed a la facon de a short dictionary, the different items following the alphabetical order. The main topics deal with the structure of simple Lie superalgebras and their finite dimensional representations; rather naturally, a few pages are devoted to supersymmetry. This modest booklet has two ambitious goals: to be elementary and easy to use. The beginner is supposed to find out here the main concepts on superalgebras, while a more experimented theorist should recognize the necessary tools and informations for a specific use.