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

Fuente: arXiv
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Hauptverfasser: Zhou, Kecheng, Kang, Chuangchuang, Lü, Jiafeng
Format: Preprint
Veröffentlicht: 2025
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_version_ 1866915343904014336
author Zhou, Kecheng
Kang, Chuangchuang
Lü, Jiafeng
author_facet Zhou, Kecheng
Kang, Chuangchuang
Lü, Jiafeng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_12690
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras
Zhou, Kecheng
Kang, Chuangchuang
Lü, Jiafeng
Rings and Algebras
17A40, 16T10, 17A30, 17A42, 17B10, 17B63
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.
title Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras
topic Rings and Algebras
17A40, 16T10, 17A30, 17A42, 17B10, 17B63
url https://arxiv.org/abs/2506.12690