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arXiv · 2503.15687

On conservative algebras of 2-dimensional Algebras

Hassan Oubba
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Abstract

In 1990 Kantor introduced the conservative algebra $\mathcal{W}(n)$ of all algebras (i.e. bilinear maps) on the $n$-dimensional vector space. In case $n >1$ the algebra $\mathcal{W}(n)$ does not belong to well known classes of algebras (such as associative, Lie, Jordan, Leibniz algebras). We describe $\frac{1}{2}$derivations, local (resp. $2$-local) $\frac{1}{2}$-derivations and biderivations of $\mathcal{W}(2)$. We also study similar problems for the algebra $\mathcal{W}_2$ of all commutative algebras on the two-dimensional vector space and the algebra $\mathcal{S}_2$ of all commutative algebras with trace zero multiplication on the two-dimensional space.

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Hassan Oubba. 2025-03-19. On conservative algebras of 2-dimensional Algebras. https://arxiv.org/abs/2503.15687

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