Clover nil restricted Lie algebras of quasi-linear growth

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...

g-QUASI-FROBENIUS LIE ALGEBRAS

A Lie version of Turaev’s G-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a g-quasi-Frobenius Lie algebra for g a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra (q, β) together with a left g-module structure which acts on q via derivations and for which β is g-inva...

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.