Iterated Hopf Ore extensions in positive characteristic

Brown, K. A. and Zhang, J. J. (2022) Iterated Hopf Ore extensions in positive characteristic. Journal of Noncommutative Geometry, 16(3), pp. 787-837. (doi: 10.4171/jncg/453)

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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 (PI), 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.

Item Type:Articles
Additional Information:Funding: K. A. Brown was supported by Leverhulme Emeritus Fellowship EM-2017- 081-9 and J. J. Zhang by the US National Science Foundation (Nos. DMS-1700825 and DMS-2001015)
Keywords:Geometry and Topology, Mathematical Physics, Algebra and Number Theory
Glasgow Author(s) Enlighten ID:Brown, Professor Ken
Authors: Brown, K. A., and Zhang, J. J.
College/School:College of Social Sciences
Journal Name:Journal of Noncommutative Geometry
Publisher:European Mathematical Society
ISSN (Online):1661-6960
Published Online:13 September 2022
Copyright Holders:Copyright © 2022 European Mathematical Society
First Published:First published in Journal of Noncommutative Geometry 16(3): 787-837
Publisher Policy:Reproduced under a Creative Commons License

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