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.
Categories: math.RT