Pointed p³-dimensional Hopf algebras in positive characteristic

2016/09/13 by Van C. Nguyen, Nguyen, Van C., Xingting Wang +1
Mathematics · Physics and Astronomy · #16T05 #17B60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.RA #msc:16T05 #msc:17B60

paper · pdf · doi:10.48550/arxiv.1609.03952

40 pages, 1 figure and 2 tables; comments and suggestions are welcome

arxiv created 2016/09/13 · openalex publication_date 2016/09/13 · arxiv updated 2016/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify pointed p³-dimensional Hopf algebras H over any algebraically closed field k of prime characteristic p>0. In particular, we focus on the cases when the group G(H) of group-like elements is of order p or p², that is, when H is pointed but is not connected nor a group algebra. This work provides many new examples of (parametrized) non-commutative and non-cocommutative finite-dimensional Hopf algebras in positive characteristic.

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