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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.19749 |
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| _version_ | 1866915877433114624 |
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| author | Ma, Tianshui Ming, Yuguang Zhao, Chan |
| author_facet | Ma, Tianshui Ming, Yuguang Zhao, Chan |
| contents | This paper studies bialgebraic structures associated with a Reynolds Leibniz algebra of weight $λ$, that is, a Leibniz algebra equipped with a Reynolds operator of weight $λ$. We first present equivalent characterizations of Reynolds Leibniz bialgebras of weight $λ$, using matched pairs and Manin triples. Next, we examine compatibility conditions between solutions of the classical Leibniz Yang-Baxter equation and Reynolds operators of weight $λ$, framed in terms of triangular Reynolds Leibniz bialgebras. Finally, building on results of Ayupov {\em et al.}, we classify two-dimensional triangular Reynolds Leibniz bialgebras of weight $λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19749 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reynolds Leibniz bialgebras of any weight Ma, Tianshui Ming, Yuguang Zhao, Chan Rings and Algebras This paper studies bialgebraic structures associated with a Reynolds Leibniz algebra of weight $λ$, that is, a Leibniz algebra equipped with a Reynolds operator of weight $λ$. We first present equivalent characterizations of Reynolds Leibniz bialgebras of weight $λ$, using matched pairs and Manin triples. Next, we examine compatibility conditions between solutions of the classical Leibniz Yang-Baxter equation and Reynolds operators of weight $λ$, framed in terms of triangular Reynolds Leibniz bialgebras. Finally, building on results of Ayupov {\em et al.}, we classify two-dimensional triangular Reynolds Leibniz bialgebras of weight $λ$. |
| title | Reynolds Leibniz bialgebras of any weight |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2603.19749 |