1. Structure of Basic Lie Superalgebras and of their Affine Extensions
- Author
-
P. Sorba, Luc Frappat, A. Sciarrino, L., Frappat, Sciarrino, Antonino, and P., Sorba
- Subjects
Mathematics::Rings and Algebras ,Real form ,Statistical and Nonlinear Physics ,Lie superalgebra ,Killing form ,Kac–Moody algebra ,Superalgebra ,Affine Lie algebra ,Graded Lie algebra ,Algebra ,17A70 ,Dynkin diagram ,affine superalgebra ,Mathematics::Quantum Algebra ,17B40 ,17B70 ,Fundamental representation ,sub.superalgebra ,supersymmetry ,Mathematics::Representation Theory ,Mathematical Physics ,Mathematics - Abstract
We generalize to the case of superalgebras several properties of simple Lie algebras involving the use of Dynkin diagrams. If to a simple Lie algebra can be associated one Dynkin diagram, it is a finite set of nonequivalent 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 affine B.S.A. and use their symmetries to construct the twisted basic superalgebras.
- Published
- 1989