Outer Automorphism Groups of Contragredient Lie Superalgebras

Abstract

Let $\mathfrak {g}$ be a complex contragredient Lie superalgebra, and let D be its distinguished extended Dynkin diagram. Let $\text {Aut}(\mathfrak {g})$ be the automorphism group of $\mathfrak {g}$ , and let $\text {Int}(\mathfrak {g})$ be its identity component. We prove that $\text {Aut}(\mathfrak {g})/\text {Int}(\mathfrak {g}) \cong \text {Aut}(\mathrm {D})$ .