Finite dimensional Nichols algebras over Suzuki algebra II: over simple Yetter-Drinfeld modules of $A_{N\,2n+1}^{\mu\lambda}$
Abstract
In this paper, the author gives a complete set of simple Yetter-Drinfeld modules over Suzuki algebra $A_{N\,2n+1}^{\mu\lambda}$ 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2021
- DOI:
- arXiv:
- arXiv:2103.06475
- Bibcode:
- 2021arXiv210306475S
- Keywords:
-
- Mathematics - Quantum Algebra;
- 16T05;
- 16T25;
- 17B22
- E-Print:
- 23 Pages