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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.16450 |
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| _version_ | 1866909741940211712 |
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| author | Gubarev, Vsevolod Mashurov, Farukh Panasenko, Alexander |
| author_facet | Gubarev, Vsevolod Mashurov, Farukh Panasenko, Alexander |
| contents | There is a well-known construction of a Jordan algebra via a sharped cubic form. We introduce a generalized sharped cubic form and prove that the split spin factor algebra is induced by this construction and satisfies the identity $((a,b,c),d,b) + ((c,b,d),a,b) + ((d,b,a),c,b) = 0$. The split spin factor algebras have recently appeared in the classification of 2-generated axial algebras of Monster type fulfilled by T. Yabe; their properties were studied by J. McInroy and S. Shpectorov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16450 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized sharped cubic form and split spin factor algebra Gubarev, Vsevolod Mashurov, Farukh Panasenko, Alexander Rings and Algebras There is a well-known construction of a Jordan algebra via a sharped cubic form. We introduce a generalized sharped cubic form and prove that the split spin factor algebra is induced by this construction and satisfies the identity $((a,b,c),d,b) + ((c,b,d),a,b) + ((d,b,a),c,b) = 0$. The split spin factor algebras have recently appeared in the classification of 2-generated axial algebras of Monster type fulfilled by T. Yabe; their properties were studied by J. McInroy and S. Shpectorov. |
| title | Generalized sharped cubic form and split spin factor algebra |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2308.16450 |