A quick proof of the classification of real Lie superalgebras

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 $({\mathfrak{g}}_C,{\mathfrak{h}}_{\bar{0}},{△}^{+})$, where ${\mathfrak{g}}_C$ is a real Lie superalgebra, ${\mathfrak{h}}_{\bar{0}}$ cartan subalgebra, ${△}^{+}$ 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.

References in corpus (2)

• Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs
• Vogan diagrams of hyperbolic Kac-Moody algebras

Cited by in corpus (1)

• Vogan diagrams of Affine Kac-Moody Superalgebras