Inner Ideals of the Real Five-Dimensional Lie Algebras with Two-Dimensional Derived, Such That l′ ⊈ z

Abstract— Inner ideal of the five-dimensional non-commutative Lie alge- bras over the real fields with two-dimensional derived were classified. It is proved that one, two, three and four-dimensional inner ideals are exist in every five-dimensional Lie algebra. It is also proved that five-dimensional Lie algebras contain inner ideals which are neither ideals nor sub-algebras