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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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Table of 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 $λ$.