Cohomology of generalized 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...

The Cohomology of Restricted Lie Algebras and of Hopf Algebras

Introduction. In theory, the bar construction suffices to calculate the homology groups of an augmented algebra. In practice, the bar construction is generally too large (has too many generators) to allow computation of higher-dimensional homology groups. In this paper, we outline a procedure which simplifies the calculation of the homology and cohomology of Hopf algebras. Let i b e a (graded) ...

The Cohomology of Restricted Lie Algebras and of Hopf Algebras132

In theory, the bar construction suflices to calculate the homology groups of an augmented algebra. In practice, the bar construction is generally too large (has too many generators) to allow computation of higher dimensional homology groups. In this paper, we develop a procedure which simplifies the calculation of the homology and cohomology of Hopf algebras. Let A be a (graded) Hopf algebra ov...

N ov 2 00 1 Cohomology of Restricted Lie Algebras

Cohomology of Lie groups and Lie algebras

The aim of this expository essay is to illustrate one example of a local-to-global phenomenon. What we mean by that is better illustrated by explaining the topic at hand. We aim to understand the de Rham cohomology groups of a Lie group. But instead of doing it using actual differential forms, we shall use the properties of a Lie group (especially the fact that it is a group) to reduce calculat...