A classification of pre-Lie $H$-pseudoalgebras of low ranks
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917027240738816 |
|---|---|
| author | Gai, Botong |
| author_facet | Gai, Botong |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A classification of pre-Lie $H$-pseudoalgebras of low ranks Gai, Botong Rings and Algebras 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. |
| title | A classification of pre-Lie $H$-pseudoalgebras of low ranks |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2510.17213 |