Outer automorphism groups of real forms of contragredient Lie superalgebras

Abstract

Let g be a real form of a contragredient Lie superalgebra. Let Aut(g) be the group of g-automorphisms, and let Int(g) be its identity component. We define the outer automorphism group of g by Out(g)=Aut(g)/Int(g). The Kac diagrams are generalizations of Dynkin diagrams, and they represent the even part g0¯. The Cartan automorphisms are generalizations of Cartan involutions, and they represent g. We express Out(g) in terms of diagram symmetries on the Kac diagrams and Cartan automorphisms. As a result, we obtain Out(g) for all real forms of contragredient Lie superalgebras.