Pre-Lie 2-bialgebras and 2-grade classical Yang-Baxter equations
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908273560518656 |
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| author | Liu, Jiefeng Yue, Tongtong Wang, Qi |
| author_facet | Liu, Jiefeng Yue, Tongtong Wang, Qi |
| contents | We introduce a notion of a para-Kähler strict Lie 2-algebra, which can be viewed as a categorification of a para-Kähler Lie algebra. In order to study para-Kähler strict Lie 2-algebra in terms of strict pre-Lie 2-algebras, we introduce the Manin triples, matched pairs and bialgebra theory for strict pre-Lie 2-algebras and the equivalent relationships between them are also established. By means of the cohomology theory of Lie 2-algebras, we study the coboundary strict pre-Lie 2-algebras and introduce 2-graded classical Yang-Baxter equations in strict pre-Lie 2-algebras. The solutions of the 2-graded classical Yang-Baxter equations are useful to construct strict pre-Lie 2-algebras and para-Kähler strict Lie 2-algebras. In particular, there is a natural construction of strict pre-Lie 2-bialgebras from the strict pre-Lie 2-algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_14165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pre-Lie 2-bialgebras and 2-grade classical Yang-Baxter equations Liu, Jiefeng Yue, Tongtong Wang, Qi Quantum Algebra 17D25, 17B38, 18A05 We introduce a notion of a para-Kähler strict Lie 2-algebra, which can be viewed as a categorification of a para-Kähler Lie algebra. In order to study para-Kähler strict Lie 2-algebra in terms of strict pre-Lie 2-algebras, we introduce the Manin triples, matched pairs and bialgebra theory for strict pre-Lie 2-algebras and the equivalent relationships between them are also established. By means of the cohomology theory of Lie 2-algebras, we study the coboundary strict pre-Lie 2-algebras and introduce 2-graded classical Yang-Baxter equations in strict pre-Lie 2-algebras. The solutions of the 2-graded classical Yang-Baxter equations are useful to construct strict pre-Lie 2-algebras and para-Kähler strict Lie 2-algebras. In particular, there is a natural construction of strict pre-Lie 2-bialgebras from the strict pre-Lie 2-algebras. |
| title | Pre-Lie 2-bialgebras and 2-grade classical Yang-Baxter equations |
| topic | Quantum Algebra 17D25, 17B38, 18A05 |
| url | https://arxiv.org/abs/2503.14165 |