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The main objective of this paper is to provide the tool rather than the classical adjoint representation of Lie algebra; which is essential in the conception of the Chevalley Eilenberg Cohomology. We introduce the notion of representation induced by a 2 -3 matrix. We construct the corresponding Chevalley Eilenberg differential and we compute all its cohomological groups.doi:10.4236/apm.2015.514078 fatcat:2jb7wufhejh6rf6d7pgbvixm4y