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arXiv · 2601.11168

The symmetric operation in a free Novikov algebra

Askar Dzhumadil'daev·Nurlan Ismailov
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Abstract

We study the symmetrization of the Novikov product. Using the embedding of a free Novikov algebra into a commutative differential algebra over a field of characteristic zero, we first obtain a basis for the subalgebra generated by the free generators with respect to the symmetrized product $a\circ b=ab+ba$. Next, using Euler operators (variational derivatives), we give a criterion for recognizing symmetric elements and show that these elements coincide with null Lagrangians in the corresponding differential realization. We then construct a non-special homomorphic image and show that the class of algebras embeddable into symmetrizations of Novikov algebras does not form a variety. Finally, we determine the module structure of the multilinear components over the symmetric group.

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Askar Dzhumadil'daev, Nurlan Ismailov. 2026-01-16. The symmetric operation in a free Novikov algebra. https://arxiv.org/abs/2601.11168

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