Iterated Hopf Ore extensions in positive characteristic

Journal of noncommutative geometry

article

Kenneth A. Brown¹  James J. Zhang² 

[1] University of Glasgow;University of Washington

关键词: Hopf Ore extension;    Ore extension;    Hopf algebra;    PBW deformation;    Nakayama automorphism;    positive characteristic;    polynomial identity;   

DOI  :  10.4171/jncg/453

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

Iterated Hopf Ore extensions (IHOEs) over an algebraically closed base field k\Bbbkk of positive characteristic ppp are studied. We show that every IHOE over k\Bbbkk satisfies a polynomial identity (PI), with PI-degree a power of ppp, and that it is a filtered deformation of a commutative polynomial ring. We classify all 222-step IHOEs over k\Bbbkk, thus generalising the classification of 222-dimensional connected unipotent algebraic groups over k\Bbbkk. Further properties of 222-step IHOEs are described: for example their simple modules are classified, and every 222-step IHOE is shown to possess a large Hopf center and hence an analog of the restricted enveloping algebra of a Lie k\Bbbkk-algebra. As one of a number of questions listed, we propose that such a restricted Hopf algebra may exist for every IHOE over k\Bbbkk.

【 授权许可】

CC BY