@article{Li2023, 
author = {Kangqiao Li and Gongxiang Liu},
title = {Finite duals of affine prime regular Hopf algebras of GK-dimension one},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {6829-6879},
keywords = {Hopf algebra, prime, GK-dimension one, finite dual, regular, Hopf pairing},
url = {https://www.sciopen.com/article/10.3934/math.2023347},
doi = {10.3934/math.2023347},
abstract = {This paper is an attempt to construct a special kind of Hopf pairing    ⟨  −  ,  −  ⟩  :      H    ∙    ⊗  H  →    . Specifically,        H    ∙   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    ∘   of them, which are given by generators and relations; 2) the Hopf pairings desired are determined by choosing certain Hopf subalgebras        H    ∙   of        H    ∘  , where    ⟨  −  ,  −  ⟩ becomes the evaluation.}
}