Representation of Lie Groups and Algebras with Applications in Differential Equations and Harmonic Oscillators.

Abstract

This paper presents the representation of Lie groups and Lie algebras with precisely two areas
of its applications. We starting on the level of explaining the basic concept of Lie groups, which
we then review some connections between Lie groups and Lie algebras and then to their
representation and we finally considered its applications in differential equations and
harmonic oscillators and currents.