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arXiv · 2511.19293

Noetherian pointed Hopf algebras are affine

Huan Jia·Yinhuo Zhang
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Abstract

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.

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Huan Jia, Yinhuo Zhang. 2025-11-24. Noetherian pointed Hopf algebras are affine. https://arxiv.org/abs/2511.19293

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