Abstract
<abstract><p>This paper is an attempt to construct a special kind of Hopf pairing $ \langle-, -\rangle:H^\bullet\otimes H\rightarrow {𝕜} $. 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.</p></abstract>
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