Semisimple Hopf algebras of dimension 2q³

2011/05/23 by Jingcheng Dong, Li Dai, Dong, Jingcheng +1
Mathematics · Physics and Astronomy · #16W30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1105.4398

openalex publication_date 2011/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q be a prime number, k an algebraically closed field of characteristic 0, and H a non-trivial semisimple Hopf algebra of dimension 2q³. This paper proves that H can be constructed either from group algebras and their duals by means of extensions, or from Radford's biproduct H≅ R#kG, where kG is the group algebra of G of order 2, R is a semisimple Yetter-Drinfeld Hopf algebra in ^kG_kGYD of dimension q³.

Citations

• Normal basis and transitivity of crossed products for Hopf algebras

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