论文标题
铃木代数I上方的有限尺寸nichols代数：$ a_ {n \，2n}^{μλ} $的简单Yetter-drinfeld模块
Finite dimensional Nichols algebras over Suzuki algebra I: simple Yetter-Drinfeld modules of $A_{N\,2n}^{μλ}$
论文作者
论文摘要
Suzuki代数$ a_ {nn}^{μλ} $是由Suzuki Satoshi在1998年引入的，这是一类Cosemisimple Hopf代数。通常，它与总体代数相同。在本文中，作者在铃木代数$ a_ {n \，2n}^{μλ} $上提供了一组简单的Yetter-Drinfeld模块，并在这些简单的Yetter-Drinfeld模块上调查了Nichols代数。对角线类型的有限尺寸尼科尔斯代数是cartan型$ a_1 $，$ a_1 \ times a_1 $，$ a_2 $，$ a_2 \ times a_2 $，super Type $ {\ bf a}有$ 64 $，$ 4M $和$ m^2 $ - 维尼古尔斯代数，非二角形类型，$ a_ {n \，2n}^{μλ} $。 $ 64 $ - 维尼科尔斯代数为二面架的类型$ \ bbb {d} _4 $。 $ 4M $和$ M^2 $ -Dimensional Nichols代数$ \ Mathfrak {b}（v_ {abe}）$首先是由Andruskiewitsch和Giraldi发现的，可以在$ a_ {nn}^nn}^nn}^$ a_ a_ a__ {nn}^$ a________的类别中实现。通过使用Masuoka的结果，我们证明了$ \ dim \ mathfrak {b}（v_ {abe}）= \ infty $在条件下$ b^2 =（ae）^{ - 1} $，$ b \ in \ bbb {g}
The Suzuki algebra $A_{Nn}^{μλ}$ was introduced by Suzuki Satoshi in 1998, which is a class of cosemisimple Hopf algebras. It is not categorically Morita-equivalent to a group algebra in general. In this paper, the author gives a complete set of simple Yetter-Drinfeld modules over the Suzuki algebra $A_{N\,2n}^{μλ}$ and investigates the Nichols algebras over those simple Yetter-Drinfeld modules. The involved finite dimensional Nichols algebras of diagonal type are of Cartan type $A_1$, $A_1\times A_1$, $A_2$, $A_2\times A_2$, Super type ${\bf A}_{2}(q;I_2)$ and the Nichols algebra ufo(8). There are $64$, $4m$ and $m^2$-dimensional Nichols algebras of non-diagonal type over $A_{N\,2n}^{μλ}$. The $64$-dimensional Nichols algebras are of dihedral rack type $\Bbb{D}_4$. The $4m$ and $m^2$-dimensional Nichols algebras $\mathfrak{B}(V_{abe})$ discovered first by Andruskiewitsch and Giraldi can be realized in the category of Yetter-Drinfeld modules over $A_{Nn}^{μλ}$. By using a result of Masuoka, we prove that $\dim\mathfrak{B}(V_{abe})=\infty$ under the condition $b^2=(ae)^{-1}$, $b\in\Bbb{G}_{m}$ for $m\geq 5$.
