Some results of representation for lie algebras.

Lie algebras appeared in mathematics at the end of the 19th century in connection with the study of Lie groups. A Lie algebra is a vector space over some field together with a bilinear multiplication is called the bracket which satisfies two simple properties: skew symmetric and Jacobi identity. The universal property of tensor product for representations of Lie algebras is a supporting conjugate of tensor product, which guarantees obtaining a linear map from a bilinear map. The main objective of the paper is to obtain results in representations for Lie algebra through the new structure consisting of four and five representations, by action of representation for Lie algebra. As well as obtaining new generalizations using dual action of representation for Lie algebra. [ABSTRACT FROM AUTHOR]