Nijenhuis pre-Lie bialgebras, Nijenhuis Lie bialgebras and \sss-equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916880749428736 |
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| author | Guo, Li Ma, Tianshui |
| author_facet | Guo, Li Ma, Tianshui |
| contents | Two aspects on the important notion of pre-Lie algebras are pre-Lie bialgebras (or left-symmetric bialgebras) with motivation from para-Kähler Lie algebras, and Nijenhuis operators on pre-Lie algebras arising from their deformation theory. In this paper, we present a method to construct Nijenhuis operators on a pre-Lie algebras via pseudo-Hessian pre-Lie algebras. Next, we introduce the notion of Nijenhuis operators on pre-Lie coalgebras and give their constructions, one from a linearly compatible pre-Lie coalgebra structure, and one from pre-Lie bialgebras. We then obtain a bialgebraic structure on Nijenhuis pre-Lie algebras by using dual representations and study their relations with \sss-equations and $\mathcal{O}$-operators. Finally we prove that a Nijenhuis balanced pre-Lie bialgebra produces a Nijenhuis Lie bialgebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nijenhuis pre-Lie bialgebras, Nijenhuis Lie bialgebras and \sss-equation Guo, Li Ma, Tianshui Quantum Algebra Representation Theory 17B38, 16T25, 17B62, 16T10, 17A30, 37K99 Two aspects on the important notion of pre-Lie algebras are pre-Lie bialgebras (or left-symmetric bialgebras) with motivation from para-Kähler Lie algebras, and Nijenhuis operators on pre-Lie algebras arising from their deformation theory. In this paper, we present a method to construct Nijenhuis operators on a pre-Lie algebras via pseudo-Hessian pre-Lie algebras. Next, we introduce the notion of Nijenhuis operators on pre-Lie coalgebras and give their constructions, one from a linearly compatible pre-Lie coalgebra structure, and one from pre-Lie bialgebras. We then obtain a bialgebraic structure on Nijenhuis pre-Lie algebras by using dual representations and study their relations with \sss-equations and $\mathcal{O}$-operators. Finally we prove that a Nijenhuis balanced pre-Lie bialgebra produces a Nijenhuis Lie bialgebra. |
| title | Nijenhuis pre-Lie bialgebras, Nijenhuis Lie bialgebras and \sss-equation |
| topic | Quantum Algebra Representation Theory 17B38, 16T25, 17B62, 16T10, 17A30, 37K99 |
| url | https://arxiv.org/abs/2508.02983 |