Averaging pre-Lie bialgebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911542400778240 |
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| author | Gao, Lin Yang, Mengke Zhang, Yuanyuan |
| author_facet | Gao, Lin Yang, Mengke Zhang, Yuanyuan |
| contents | In this paper, we first introduce representations of averaging pre-Lie algebras and study their matched pairs, Manin triples, and bialgebra theories. We prove that these three notions are equivalent under certain conditions. Moreover, by introducing averaging operators on quadratic Rota-Baxter pre-Lie algebras, we show that such operators give rise to averaging pre-Lie bialgebras. Then we introduce the notion of admissible classical Yang-Baxter equations in averaging pre-Lie algebras, as well as the relative Rota-Baxter operators on averaging pre-Lie algebras, and show that the relative Rota-Baxter operators on averaging pre-Lie algebras yield symmetric solutions of admissible classical Yang-Baxter equations in averaging pre-Lie algebras. Finally, we show that every averaging pre-Lie bialgebra induces an averaging Lie bialgebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10671 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Averaging pre-Lie bialgebras Gao, Lin Yang, Mengke Zhang, Yuanyuan Rings and Algebras Representation Theory 16W99, 17B38, 16T10 In this paper, we first introduce representations of averaging pre-Lie algebras and study their matched pairs, Manin triples, and bialgebra theories. We prove that these three notions are equivalent under certain conditions. Moreover, by introducing averaging operators on quadratic Rota-Baxter pre-Lie algebras, we show that such operators give rise to averaging pre-Lie bialgebras. Then we introduce the notion of admissible classical Yang-Baxter equations in averaging pre-Lie algebras, as well as the relative Rota-Baxter operators on averaging pre-Lie algebras, and show that the relative Rota-Baxter operators on averaging pre-Lie algebras yield symmetric solutions of admissible classical Yang-Baxter equations in averaging pre-Lie algebras. Finally, we show that every averaging pre-Lie bialgebra induces an averaging Lie bialgebra. |
| title | Averaging pre-Lie bialgebras |
| topic | Rings and Algebras Representation Theory 16W99, 17B38, 16T10 |
| url | https://arxiv.org/abs/2602.10671 |