From the theory of finite dimensional Lie algebras it is known that every
finite dimensional Lie algebra is decomposed into a semidirect sum of
semisimple subalgebra and solvable radical. Moreover, due to work of Mal'cev
the study of solvable Lie algebras is reduced to the study of nilpotent ones.
For the finite dimensional Leibniz algebras the analogues of the mentioned
results are not proved yet. In order to get some idea how to establish the
results we examine the Leibniz algebra for which the quotient algebra with
respect to the ideal generated by squares elements of the algebra (denoted by
I) is a semidirect sum of semisimple Lie algebra and the maximal solvable
ideal. In this paper the class of complex Leibniz algebras, for which quotient
algebras by the ideal I are isomorphic to the semidirect sum of the algebra
sl2​ and two-dimensional solvable ideal R, are described.Comment: 11 page