Restricted Lie algebras with semilinear $p$-mappings

Restricted Lie Algebras

REPRESENTATIONS OF RESTRICTED LIE ALGEBRAS OF CHARACTERISTIC p

It was proved by Jacobson [2] that every finite-dimensional Lie algebra of characteristic p has a finite-dimensional representation space which is not semisimple. In this note we prove a similar result for Jacobson's restricted Lie algebras [l]. The structure of a restricted Lie algebra L over a field F of characteristic p comprises, in addition to the ordinary Lie algebra structure, a map x—*-...

Cohomology of Restricted Lie Algebras

In this dissertation, we investigate the cohomology theory of restricted Lie algebras. Motivations for the definition of a restricted Lie algebra are given and the theory of ordinary Lie algebra cohomology is briefly reviewed, including a discussion on algebraic interpretations of the low dimensional cohomology spaces of ordinary Lie algebras. The general Cartan-Eilenberg construction of the st...

Deformations of Simple Restricted Lie Algebras I

We compute the infinitesimal deformations of two families of simple restricted modular Lie algebras of Cartan-type: the Witt-Jacobson and the Special Lie algebras.

Deformations of Restricted Simple Lie Algebras I

We compute the infinitesimal deformations of two families of simple restricted modular Lie algebras of Cartan-type: the Witt-Jacobson and the Special Lie algebras.