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arXiv · 2510.17213

A classification of pre-Lie $H$-pseudoalgebras of low ranks

Botong Gai
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Abstract

Let $H=U(\delta)$ be the universal enveloping algebra of finite dimension Lie algebra $\delta$. 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.

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Botong Gai. 2025-10-20. A classification of pre-Lie $H$-pseudoalgebras of low ranks. https://arxiv.org/abs/2510.17213

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