On conservative algebras of 2-dimensional Algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913747270893568 |
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| author | Oubba, Hassan |
| author_facet | Oubba, Hassan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15687 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On conservative algebras of 2-dimensional Algebras Oubba, Hassan Rings and Algebras 15A69, 17A30, 17B40, 17B63, 17D10 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. |
| title | On conservative algebras of 2-dimensional Algebras |
| topic | Rings and Algebras 15A69, 17A30, 17B40, 17B63, 17D10 |
| url | https://arxiv.org/abs/2503.15687 |