Second cohomology of generalized Cartan type S Lie algebras in characteristic zero

Generalized Cartan Type S Lie Algebras in Characteristic 0 ( Ii )

This paper is a sequel to the paper [7] in which generalized Cartan type S Lie algebras tzS(A, T, φ) over a field F of characteristic 0 were studied. We have tried to make this paper independent of other papers. So in Section 2, we give a description of relevant Lie algebras and some basic facts which will be used in this paper. In Section 3 we introduce a class of Lie algebras which are subalg...

Second Hochschild Cohomology of Convolution Algebras

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...

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...