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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.17213 |
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Table of Contents:
- Let $H=U(δ)$ be the universal enveloping algebra of finite dimension Lie algebra $δ$. The central result of the paper is the classification of pre-Lie $H$-pseudoalgebras of low ranks over the Hopf algebra $H$. We firstly study pre-Lie pseudoalgebras that are free of rank $1$ over $H$. Then we introduce and classify a class of pre-Lie $H$-pseudoalgebras $\mathcal{P}$ which are generated by two pre-Lie pseudoalgebras of rank $1$. Finally, the associativity of $\mathcal{P}$ is also considered and a explicit assification is presented.