Solvable Leibniz algebras with triangular nilradicals

In this paper the description of solvable Lie algebras with triangular nilradicals is extended to Leibniz algebras. It is proven that the matrices of the left and the right operators on the elements of Leibniz algebra have the upper triangular forms. We establish that solvable Leibniz algebra of a maximal possible dimension with a given triangular nilradical is a Lie algebra. Furthermore, solvable Leibniz algebras with triangular nilradicals of the low dimensions are classified.