Structure of Basic Lie Superalgebras and of Their Affine Extensions.

摘要

We generalize to the case of superalgebras several properties of simple Lie algebras involving the use of Dynkin diagrams. If a simple Lie algebra can be associated with one Dynkin diagram, it is a finite set of non equivalent ones which can be constructed for a basic superalgebra (or B.S.A.). The knowledge of these diagrams, which can be obtained for each B.S.A. in a systematic way, allows us to deduce the regular subsuperalgebras of a B.S.A. The symmetries of the Dynkin diagrams are related to outer automorphisms of B.S.A. and lead to some singular subsuperalgebras. Finally we consider the extended Dynkin diagrams in order to classify the related B.S.A. and use their symmetries to construct the twisted basic superalgebras. (ERA citation 13:031597)