Rota-Baxter operators of nilpotent evolution algebras with maximal nilindex
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917199625584640 |
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| author | Qaralleh, Izzat Mukhamedov, Farrukh Khakimov, Otabek |
| author_facet | Qaralleh, Izzat Mukhamedov, Farrukh Khakimov, Otabek |
| contents | Nilpotent evolution algebras of maximal nilindex admit a natural basis in which the structure matrix is strictly upper triangular. In this paper we classify Rota{Baxter operators of weights zero and one on such algebras. We prove that every Rota{Baxter operator is upper triangular with respect to a natural basis. For weight zero, a strong rigidity phenomenon occurs: the operators are diagonal up to possible perturbations supported in the last basis vector. For weight one, a richer structure appears, including both triangular and non-triangular families, with the diagonal entries governed by a rational recurrence relation. Our results provide a complete description of Rota{Baxter operators on nilpotent evolution algebras of maximal nilindex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08669 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rota-Baxter operators of nilpotent evolution algebras with maximal nilindex Qaralleh, Izzat Mukhamedov, Farrukh Khakimov, Otabek Rings and Algebras 17A60, 17A36, 17D92, 47B39 Nilpotent evolution algebras of maximal nilindex admit a natural basis in which the structure matrix is strictly upper triangular. In this paper we classify Rota{Baxter operators of weights zero and one on such algebras. We prove that every Rota{Baxter operator is upper triangular with respect to a natural basis. For weight zero, a strong rigidity phenomenon occurs: the operators are diagonal up to possible perturbations supported in the last basis vector. For weight one, a richer structure appears, including both triangular and non-triangular families, with the diagonal entries governed by a rational recurrence relation. Our results provide a complete description of Rota{Baxter operators on nilpotent evolution algebras of maximal nilindex. |
| title | Rota-Baxter operators of nilpotent evolution algebras with maximal nilindex |
| topic | Rings and Algebras 17A60, 17A36, 17D92, 47B39 |
| url | https://arxiv.org/abs/2601.08669 |