Colour algebras over rings
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914373492015104 |
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| author | Pumpluen, Susanne |
| author_facet | Pumpluen, Susanne |
| contents | Colour algebras over fields of odd characteristic are well-known noncommutative Jordan algebras. We define colour algebras more generally over a unital commutative associative ring with $\frac{1}{2}\in R$, and show that colour algebras can be constructed canonically by employing nondegenerate ternary hermitian forms with trivial determinant. We investigate their structure, automorphism group and derivations. As over fields, colour algebras over $R$ are closely related to octonion algebras over $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Colour algebras over rings Pumpluen, Susanne Rings and Algebras Colour algebras over fields of odd characteristic are well-known noncommutative Jordan algebras. We define colour algebras more generally over a unital commutative associative ring with $\frac{1}{2}\in R$, and show that colour algebras can be constructed canonically by employing nondegenerate ternary hermitian forms with trivial determinant. We investigate their structure, automorphism group and derivations. As over fields, colour algebras over $R$ are closely related to octonion algebras over $R$. |
| title | Colour algebras over rings |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2409.14574 |