A quick proof of the classification of real Lie superalgebras

TL;DR

This paper presents a rapid method for classifying real Lie superalgebras using Vogan diagrams, extending classical theorems and simplifying the classification process compared to existing approaches.

Contribution

It develops a faster classification technique for real Lie superalgebras by adapting Borel and de Seibenthal theorems with Vogan diagrams.

Findings

Introduces a quick classification method for real Lie superalgebras.

Extends classical theorems to the superalgebra context.

Provides a simplified approach compared to previous classifications.

Abstract

This article classifies the real forms of Lie Superalgebra by Vogan diagrams, developing Borel and de Seibenthal theorem of semisimple Lie algebras for Lie superalgebras. A Vogan diagram is a Dynkin diagram of triplet $(\mathfrak{g}_{C},\mathfrak{h_{\bar{0}}},\triangle^{+})$, where $\mathfrak{g}_{C}$ is a real Lie superalgebra, $\mathfrak{h_{\bar{0}}}$ cartan subalgebra, $\triangle^{+}$ positive root system. Although the classification of real forms of contragradient Lie superalgebras is already done. But our method is a quicker one to classify.