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arXiv · 2004.14702

Iterated Hopf Ore extensions in positive characteristic

Ken A. Brown·James J. Zhang
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Abstract

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.

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Ken A. Brown, James J. Zhang. 2020-04-30. Iterated Hopf Ore extensions in positive characteristic. https://arxiv.org/abs/2004.14702

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