A classification of 2-dimensional endo-commutative straight algebras of type II_1
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913247918030848 |
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| author | Takahasi, Sin-Ei Shirayanagi, Kiyoshi Tsukada, Makoto |
| author_facet | Takahasi, Sin-Ei Shirayanagi, Kiyoshi Tsukada, Makoto |
| contents | In this paper, we present a complete classification of 2-dimensional endo-commutative straight algebras of type II$_1$ over any field. An endo-commutative algebra is a non-associative algebra in which the square mapping preserves multiplication. A 2-dimensional straight algebra satisfies the condition that there exists an element $x$ such that $x$ and $x^2$ are linearly independent. The term type II$_1$ denotes a distinguishing characteristic of its structure matrix, which has rank 2. We provide multiplication tables for these algebras, listing them up to isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A classification of 2-dimensional endo-commutative straight algebras of type II_1 Takahasi, Sin-Ei Shirayanagi, Kiyoshi Tsukada, Makoto Rings and Algebras 17A30 (Primary) 17D99, 13A99 (Secondary) In this paper, we present a complete classification of 2-dimensional endo-commutative straight algebras of type II$_1$ over any field. An endo-commutative algebra is a non-associative algebra in which the square mapping preserves multiplication. A 2-dimensional straight algebra satisfies the condition that there exists an element $x$ such that $x$ and $x^2$ are linearly independent. The term type II$_1$ denotes a distinguishing characteristic of its structure matrix, which has rank 2. We provide multiplication tables for these algebras, listing them up to isomorphism. |
| title | A classification of 2-dimensional endo-commutative straight algebras of type II_1 |
| topic | Rings and Algebras 17A30 (Primary) 17D99, 13A99 (Secondary) |
| url | https://arxiv.org/abs/2402.18952 |