Title : Tits construction, Freudenthal Magic

Square, and modular simple Lie superalgebras.

Abstract :

The well-known construction due to Tits of the

exceptional Lie algebras in terms of a

composition algebra and a degree three simple

Jordan algebra will be reviewed. Variations of this construction

will be shown which allow to extend it to obtain

Lie superalgebras. Several new simple

Lie superalgebras over fields of low

characteristic will thus appear naturally.