Extraction Lie Algebra and Extraction Lie Derivation

Abstract

In this research paper, we discussed a new Lie algebra generated from the composition of tow direct sum, such that the result is not contained in their direct sum. We called it the Extraction Lie algebra. Then we restricted ourselves to the special class . We defined the same definition of the derivation Lie algebra and the adjoin, along with some properties, such as . And the result obtained from the derived elements always yields the zero result, as we have clarified in this paper, from the components of the Extraction Lie algebra.