On the structure of free dual Leibniz algebras

It is proved that over a field of characteristic zero the free dual Leibniz algebras are the free associative-commutative algebras (without unity) with respect to the multiplication $a\circ b = ab+ba$ and their free generators are found. We construct the examples of subalgebras of two-generated free dual Leibniz algebra, that are free dual Leibniz algebras of countable rank.