An algebra with the identity $xcirc (ycirc z-zcirc y)= (xcirc y)circ z-(xcirc z)circ y$ is called right-symmetric. A right-symmetric algebra with the identity $xcirc(ycirc z)= ycirc(xcirc z)$ is called Novikov. We describe bases of free right-symmetric algebras and free Novikov algebras and give realizations of them in terms of trees. The free Lie algebra is obtained as a Lie subalgebra of the free right-symmetric algebra. We use our methods to study identities of Witt algebras.
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机译：标识为$ x circ（y circ z-z circ y）=（x circ y） circ z-（x circ z） circ y $的代数称为右对称。标识为$ x circ（y circ z）= y circ（x circ z）$的右对称代数称为Novikov。我们描述了自由右对称代数和自由Novikov代数的基础，并以树的形式给出了它们的实现。获得自由李代数作为自由右对称代数的李子代数。我们使用我们的方法来研究维特代数的恒等式。
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