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