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arXiv · 2103.00495

The Finite Duals of Affine Prime Regular Hopf Algebras of GK-Dimension One

Kangqiao Li·Gongxiang Liu
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Abstract

This paper is an attempt to construct a special kind of Hopf pairing $\langle-,-\rangle:H^\bullet\otimes H\rightarrow\Bbbk$. Specifically, $H^\bullet$ and $H$ should be both affine, noetherian and of the same GK-dimension. In addition, some properties of them would be dual to each other. We test the ideas in two steps for all the affine prime regular Hopf algebras $H$ of GK-dimension one: 1) We compute the finite duals $H^\circ$ of them, which are given by generators and relations; 2) the Hopf pairings desired are determined by choosing certain Hopf subalgebras $H^\bullet$ of $H^\circ$, where $\langle-,-\rangle$ becomes the evaluation.

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Kangqiao Li, Gongxiang Liu. 2021-02-28. The Finite Duals of Affine Prime Regular Hopf Algebras of GK-Dimension One. https://arxiv.org/abs/2103.00495

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