2020/04/30 by Ken A. Brown, Brown, Ken A., James J. Zhang +1 · 1 citation
Mathematics · #16R50 #16S36 #16T05 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2004.14702
openalex publication_date 2020/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.