Rota-Baxter operators of nonzero weight on the split Cayley-Dickson algebra
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929697053474816 |
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| author | Panasenko, A. S. |
| author_facet | Panasenko, A. S. |
| contents | We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obtain a description of all decompositions of split octonions over a quadratically closed field of characteristic different from 2 into a sum of two subalgebras, which describes the splitting Rota-Baxter operators. It completes the classification of Rota-Baxter operators on composition algebras of any weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rota-Baxter operators of nonzero weight on the split Cayley-Dickson algebra Panasenko, A. S. Rings and Algebras 17D05, 17A36 We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obtain a description of all decompositions of split octonions over a quadratically closed field of characteristic different from 2 into a sum of two subalgebras, which describes the splitting Rota-Baxter operators. It completes the classification of Rota-Baxter operators on composition algebras of any weight. |
| title | Rota-Baxter operators of nonzero weight on the split Cayley-Dickson algebra |
| topic | Rings and Algebras 17D05, 17A36 |
| url | https://arxiv.org/abs/2502.01928 |