Z2 and Klein graded Lie algebras

TL;DR

This thesis explores Klein graded Lie algebras, extending fundamental Lie superalgebra results like Poincare-Birkhoff-Witt, Ado's theorem, and Schur's lemma, with illustrative examples.

Contribution

It introduces Klein graded Lie algebras, proves key theorems analogous to Lie superalgebras, and provides concrete examples.

Findings

Proved Poincare-Birkhoff-Witt theorem for Klein graded Lie algebras

Established Ado's theorem in the Klein graded context

Presented two explicit examples of Klein graded Lie algebras

Abstract

In this master's thesis, we recall the definitions and basic results for Lie superalgebras. We specify the definition for Klein graded Lie algebras and, motivated by well known results for Lie superalgebras, we prove similar results for Klein graded Lie algebras. More precisely, we state the theorems of Poincare-Birkhoff-Witt and Ado's, as well as Schur's lemma. Moreover, we present two examples of Klein graded algebra.