Leibniz algebras generated using the image of Euclidean algebras

Abstract

In this work we have considered about Lie and Leibniz algebras and their representations, particularly we have
learned the Euclidean algebra . For a given the Euclidean algebra and the right -module , we can construct
a Leibniz algebra. In this paper we have learned Leibniz algebras constructed by Euclidean Lie algebra and
some of its modules. We used its modules that arise from matrix realization of .