Finite dimensional Nichols algebras over Suzuki algebra II: over simple Yetter-Drinfeld modules of $A_{N2n+1}^{\mu \lambda }$

Abstract

In this paper, the author gives a complete set of simple Yetter-Drinfeld modules over Suzuki algebra $A_{N2n+1}^{\mu \lambda }$ and investigates the Nichols algebras over those irreducible Yetter-Drinfeld modules. The finite dimensional Nichols algebras of diagonal type are of Cartan type $A_1$, $A_1\times A_1$, $A_2$, Super type $A_2(q;I_2)$ and the Nichols algebra $\mathfrak{ufo}(8)$. And the involved finite dimensional Nichols algebras of non-diagonal type are $12$, $4m$ and $m^2$ dimensional. The left three unsolved cases are set as open problems.

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• Finite dimensional Nichols algebras over Suzuki algebra I: simple Yetter-Drinfeld modules of $A_{N2n}^{\mu \lambda }$