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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2404.13894 |
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| _version_ | 1866912497497276416 |
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| author | Zhang, Huhu Gao, Xing Wu, Tingzeng Feng, Xinyang |
| author_facet | Zhang, Huhu Gao, Xing Wu, Tingzeng Feng, Xinyang |
| contents | Bremner and Elgendy developed a classification of operated polynomial identities for linear operators on associative algebras, encompassing both classical and newly discovered cases. Within the framework of Rota's Program, each of these new operated associative polynomial identities was shown to be Gröbner-Shirshov. This naturally led to a question posed by Guo and collaborators: is each corresponding operated Lie polynomial identity also Gröbner-Shirshov? In this paper, we provide an affirmative answer by proving that each such Lie analogue indeed is Gröbner-Shirshov, thereby enriching the development of Rota's Program on algebraic operators within the Lie algebraic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some new operated Lie polynomial identities and Gröbner-Shirshov bases Zhang, Huhu Gao, Xing Wu, Tingzeng Feng, Xinyang Rings and Algebras 18M70, 05A05, 16W99, Bremner and Elgendy developed a classification of operated polynomial identities for linear operators on associative algebras, encompassing both classical and newly discovered cases. Within the framework of Rota's Program, each of these new operated associative polynomial identities was shown to be Gröbner-Shirshov. This naturally led to a question posed by Guo and collaborators: is each corresponding operated Lie polynomial identity also Gröbner-Shirshov? In this paper, we provide an affirmative answer by proving that each such Lie analogue indeed is Gröbner-Shirshov, thereby enriching the development of Rota's Program on algebraic operators within the Lie algebraic setting. |
| title | Some new operated Lie polynomial identities and Gröbner-Shirshov bases |
| topic | Rings and Algebras 18M70, 05A05, 16W99, |
| url | https://arxiv.org/abs/2404.13894 |