论文标题
迭代的霍夫矿石扩展是积极特征的
Iterated Hopf Ore extensions in positive characteristic
论文作者
论文摘要
研究了迭代的Hopf矿石扩展（IHOES）在代数闭合的基本k上的阳性特征P上进行了研究。我们表明，k上的每个IHOE都满足多项式身份，Pi-degree a的功率是P的功率，并且它是交换多项式环的过滤变形。我们将所有两步iHoes分类为k，从而概括了k上二维连接的一级代数组的分类。描述了2步IHOE的进一步特性：例如，它们的简单模块被分类，并且显示每个2步IHOE具有较大的HOPF中心，因此类似于lie K-Algebra的受限信封代数的类似物。作为列出的许多问题之一，我们建议每个IHOE在K上可能存在这种受限的HOPF代数。
Iterated Hopf Ore extensions (IHOEs) over an algebraically closed base field k of positive characteristic p are studied. We show that every IHOE over k satisfies a polynomial identity, with PI-degree a power of p, and that it is a filtered deformation of a commutative polynomial ring. We classify all 2-step IHOEs over k, thus generalising the classification of 2-dimensional connected unipotent algebraic groups over k. Further properties of 2-step IHOEs are described: for example their simple modules are classified, and every 2-step IHOE is shown to possess a large Hopf center and hence an analog of the restricted enveloping algebra of a Lie k-algebra. As one of a number of questions listed, we propose that such a restricted Hopf algebra may exist for every IHOE over k.
