Identities of the left-symmetric Witt algebras

Let P-n = k[x(1), x(2),..., x(n)] be the polynomial algebra over a field k of characteristic zero in the variables x(1), x(2),..., x(n) and L-n be the left-symmetric Witt algebra of all derivations of Pn [D. Burde, Left-symmetric algebras, or pre-Lie algebras in geometry and physics, Cent. Eur. J. Math. 4(3) (2006) 323-357]. We describe all right operator identities of L-n and prove that the set of all algebras L-n, where n >= 1, generates the variety of all left-symmetric algebras. We also describe a class of general (not only right operator) identities for L-n.