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 $⟨-,-⟩:H^{\bullet }\otimes H\to \mathbb{k}$. 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 $⟨-,-⟩$ becomes the evaluation.

Final version, where some errors are corrected

References in corpus (1)

• A combinatorial identity and the finite dual of infinite dihedral group algebra

Cited by in corpus (4)

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• The automorphisms group and the classification of gradings of finite dimensional associative algebras
• The finite dual coalgebra as a quantization of the maximal spectrum
• The Link-Indecomposable Components of Hopf Algebras and Their Products