A characterization of endo-commutativity of 3-dimensional curled algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918105527091200 |
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| author | Takahasi, Sin-Ei Shirayanagi, Kiyoshi |
| author_facet | Takahasi, Sin-Ei Shirayanagi, Kiyoshi |
| contents | A curled algebra is a non-associative algebra in which $x$ and $x^2$ are linearly dependent for every element $x$. An algebra is called endo-commutative, if the square mapping from the algebra to itself preserves multiplication. In this paper, we provide a necessary and sufficient condition for a 3-dimensional curled algebra over an arbitrary field to be endo-commutative, expressed in terms of the properties of its underlying linear basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A characterization of endo-commutativity of 3-dimensional curled algebras Takahasi, Sin-Ei Shirayanagi, Kiyoshi Rings and Algebras Primary 17A30, Secondary 17D99, 13A99 A curled algebra is a non-associative algebra in which $x$ and $x^2$ are linearly dependent for every element $x$. An algebra is called endo-commutative, if the square mapping from the algebra to itself preserves multiplication. In this paper, we provide a necessary and sufficient condition for a 3-dimensional curled algebra over an arbitrary field to be endo-commutative, expressed in terms of the properties of its underlying linear basis. |
| title | A characterization of endo-commutativity of 3-dimensional curled algebras |
| topic | Rings and Algebras Primary 17A30, Secondary 17D99, 13A99 |
| url | https://arxiv.org/abs/2507.20572 |