On Noetherian affine prime regular Hopf algebras of Gelfand-Kirillov dimension 1
On Noetherian affine prime regular Hopf algebras of Gelfand-Kirillov dimension 1
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DOI：
10.1090/s0002-9939-08-09034-5
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发表时间：
2008-10
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影响因子：
--
通讯作者：
Gongxiang Liu
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文献类型：
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作者：
Gongxiang Liu
令 k 为代数闭域。 2007 年，D.-M.卢，Q.-S。 Wu和J.J.Zhang提出了以下问题：除了群代数kZ、kD和无限维素数Taft代数之外，是否还有其他GK维1的诺特仿射素数正则Hopf代数？在本文中，我们给出了一个新的。卢、吴、张提出的另一个问题也可以通过这个例子来解决。假设 H 是 GK 维 1 的诺特仿射素数正则 Hopf 代数，我们证明 grH := ⊕ s≥0 J s iq /J s+1 iq 作为 Hopf 代数，与无限维素数 Taft 代数同构。这给出了无限维素数塔夫脱代数的表征。
Let k be an algebraically closed field. In 2007, D.-M. Lu, Q.-S. Wu, and J. J. Zhang asked the following question: Besides the group algebras kZ, kD and infinite dimensional prime Taft algebras, are there other noetherian affine prime regular Hopf algebras of GK-dimension 1? In this paper, we give a new one. Another problem posed by Lu, Wu, and Zhang can also be resolved by this example. Assuming H is a noetherian affine prime regular Hopf algebra of GK-dimension 1, we show that grH := ⊕ s≥0 J s iq /J s+1 iq , as a Hopf algebra, is isomorphic to an infinite dimensional prime Taft algebra. This gives a characterization of infinite dimensional prime Taft algebras.