CLASSIFICATION OF LIE SUBALGEBRAS UP TO AN INNER AUTOMORPHISM

In this paper, a useful classication of all lie sub-algebras of a given lie algebra up to an inner automorphism ispresented. this method can be regarded as an important con-nection between dierential geometry and algebra and has manyapplications in dierent elds of mathematics. after main results,we have applied this procedure for classifying the lie subalgebrasof some examples of lie algebras.