Central extensions of 2-filiform Leibniz algebras

In this paper we describe the central extensions of some nilpotent Leibniz algebras and one-dimensional central extensions (up to isomorphism) of all naturally graded 2-filiform Leibniz algebras over the field of complex numbers. It is well-know that 2-filiform Leibniz algebras which are not naturally graded have not yet studied. There are such kind of algebras in the algebras obtained along this article. Also in this work we describe some subclasses of 6-dimensional nilpotent Leibniz algebras with condition quotient algebra by two-dimensional center of the algebra is isomorphic to the four-dimensional naturally graded 2-filiform nonsplit Leibniz algebra.