Super Kac-Moody algebra: Classification theory. I (Q917674)

This article contains a good survey and approach to super Kac-Moody algebras, classification by roots and Cartan matrices and related problems. At first a list of classical super Lie algebras is given, even and odd roots are defined. Super Kac-Moody algebras then are obtained by adjoining one root to the corresponding Dynkin diagrams, the case of twisted algebras is discussed by regarding automorphisms. The following sections give a characterization by Chevalley bases, Cartan matrices and the construction of loop algebras. In a future communication representations shall be explained.