Noetherian pointed Hopf algebras are affine
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915641845350400 |
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| author | Jia, Huan Zhang, Yinhuo |
| author_facet | Jia, Huan Zhang, Yinhuo |
| contents | Let $k$ be a field. In this paper, we introduce the notions of $\textit{reduction order}$ and $\textit{reduction-factorization}$ on words, and use them to show that any right or left Noetherian pointed Hopf algebra over $k$ is affine. This result offers a partial affirmative answer to the classical affineness question for Noetherian Hopf algebras posed by Wu and Zhang \cite{WZ2003}. For a pointed Hopf algebra $H$ over $k$, we construct a well-ordered set $X$ such that: (1) $H$ is generated, as an algebra, by the subset $X_I$ of irreducible letters (with respect to the reduction order); and (2) $X_I$ is finite whenever $H$ is right Noetherian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noetherian pointed Hopf algebras are affine Jia, Huan Zhang, Yinhuo Quantum Algebra Rings and Algebras Let $k$ be a field. In this paper, we introduce the notions of $\textit{reduction order}$ and $\textit{reduction-factorization}$ on words, and use them to show that any right or left Noetherian pointed Hopf algebra over $k$ is affine. This result offers a partial affirmative answer to the classical affineness question for Noetherian Hopf algebras posed by Wu and Zhang \cite{WZ2003}. For a pointed Hopf algebra $H$ over $k$, we construct a well-ordered set $X$ such that: (1) $H$ is generated, as an algebra, by the subset $X_I$ of irreducible letters (with respect to the reduction order); and (2) $X_I$ is finite whenever $H$ is right Noetherian. |
| title | Noetherian pointed Hopf algebras are affine |
| topic | Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2511.19293 |