Finite dimensional Nichols algebras over H_c: σ₀ of Kashina

2022/07/25 by Liu, Miantao, Liu, Gongxiang, Zhou, Kun
#16E65 #16P40 #16S34 #16T05 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2207.11863

Abstract

Let H be the Hopf algebra H_c: σ₀ of Kashina [J. Algebra, 232(2000),pp.617-663]. We give all simple Yetter-Drinfel'd modules V over H, then classify all finite-dimensional Nichols algebras of V. The finite dimensional Nichols algebras of diagonal type are either A₁, A₂ or quantum planes, and non-diagonal type ones are 8 or 16 dimensional.

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