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arXiv · 2506.12690

Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras

Kecheng Zhou·Chuangchuang Kang·Jiafeng Lü
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Abstract

Double construction bialgebras for Poisson 3-Lie algebras and transposed Poisson 3-Lie algebras are defined and studied using matched pairs. Poisson 3-Lie algebras and transposed Poisson 3-Lie algebras are constructed on direct sums and tensor products of vector spaces. Matched pairs, Manin triples, and double construction Poisson 3-Lie bialgebras are shown to be equivalent. Since the double construction approach does not apply to bialgebra theory for transposed Poisson 3-Lie algebras, admissible transposed Poisson 3-Lie algebras are introduced. These algebras are both transposed Poisson 3-Lie algebras and Poisson 3-Lie algebras. An equivalence between matched pairs and double construction admissible transposed Poisson 3-Lie bialgebras is established.

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Kecheng Zhou, Chuangchuang Kang, Jiafeng Lü. 2025-06-15. Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras. https://arxiv.org/abs/2506.12690

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