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arXiv · 2512.12282

Polynomial Identities and Codimensions of Two- and Three-Dimensional Metabelian Non-Lie Leibniz Algebras

Luis Fertunani·Claudemir Fideles·Airton Muniz
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Abstract

Over an arbitrary field, we conduct a comprehensive study of the polynomial identities and codimensions of two- and three-dimensional metabelian non-Lie Leibniz algebras. In addition, we compute the images of multihomogeneous polynomials on two-dimensional Leibniz algebras and, as a consequence, prove that the image of any multilinear polynomial evaluated on such algebras is always a vector space. Our analysis includes the three nontrivial isomorphism classes in dimension two and the ten isomorphism classes in dimension three, all of which are metabelian. In particular, we determine finite bases for their corresponding $T$-ideals and provide explicit bases for the associated relatively free graded algebras.

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Luis Fertunani, Claudemir Fideles, Airton Muniz. 2025-12-13. Polynomial Identities and Codimensions of Two- and Three-Dimensional Metabelian Non-Lie Leibniz Algebras. https://arxiv.org/abs/2512.12282

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