Projective Modules and Blocks of Supersolvable Restricted Lie Algebras

Simple Restricted Modules For the Restricted Contact Lie Algebras

It is shown that, with a few exceptions, the simple restricted modules for a restricted contact Lie algebra are induced from those for the homogeneous component of degree zero. In [3], Shen constructed the simple restricted modules for the restricted Witt, special and hamiltonian Lie algebras which comprise three of the four classes of restricted Lie algebras of Cartan type. His methods, howeve...

Simple modules for the restricted Cartan type Lie algebras

The simple modules with homogeneous characters are considered, their dimension formulas are determined.

Some Simple Modules for the Restricted Cartan-type Lie Algebras

Every simple module having character height at most one for a restricted Cartantype Lie algebra g can be realized as a quotient of a module obtained by starting with a simple module S for the homogeneous component of degree zero in the natural grading of g, extending the action trivially to positive components and inducing up to g. It is shown that if S is not restricted, or if it is restricted...

Restricted Lie Algebras

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...