Weight Spaces of Lie Algebra Modules

Lie Algebra Modules with Finite Dimensional Weight Spaces, I

Let g denote a reductive Lie algebra over an algebraically closed field of characteristic zero, and let I) denote a Cartan subalgebra of g. In this paper we study finitely generated g-modules that decompose into direct sums of finite dimensional l)-weight spaces. We show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of ir...

Biquaternions Lie Algebra and Complex-Projective Spaces

                   .

On Lie algebra crossed modules

The goal of this article is to construct a crossed module representing the cocycle 〈[, ], 〉 generating H(g; C) for a simple complex Lie algebra g.

biquaternions lie algebra and complex-projective spaces

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...

Vertex Operator Algebra Structure of Standard Affine Lie Algebra Modules