Speciality of Metabelian Mal"tsev Algebras

It is proved that, for any metabelian Mal'tsev algebra $M$ over a field of characteristic $\ne2,3$, there is an alternative algebra $A$ such that the algebra $M$ can be embedded in the commutator algebra $A^{(-)}$. Moreover, the enveloping alternative algebra $A$ can be found in the variety of algebras with the identity $[x,y][z,t]=0$. The proof of this result is based on the construction of additive bases of the free metabelian Mal"tsev algebra and the free alternative algebra with the identity $[x,y][z,t] = 0$.