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Trees, Free Right-Symmetric Algebras, Free Novikov Algebras and Identities

Askar Dzhumadil'daev and Clas Löofwall

An algebra with the identity $x\circ (y\circ z-z\circ y)= (x\circ y)\circ z-(x\circ z)\circ y$ is called right-symmetric. A right-symmetric algebra with the identity $x\circ(y\circ z)= y\circ(x\circ z)$ 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.

Homology, Homotopy and Applications, Vol. 4(2), 2002, pp. 165-190

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