Finite-dimensional Nichols algebras over the Suzuki algebras I: simple Yetter-Drinfeld modules of AµλN 2n.

The Suzuki algebra AµλNn, introduced by Suzuki Satoshi in 1998, 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 AµλN2n and investigates the Nichols algebras over those simple Yetter-Drinfeld modules. The involved finite dimensional Nichols algebras of diagonal type are of Cartan type A1, A1 × A1, A2, A2 × A2, Super type A2(q; I2) and the Nichols algebra ufo(8). There are 64, 4m and m² -dimensional Nichols algebras of non-diagonal type over AµλN2n . The 64-dimensional Nichols algebras are of dihedral rack type D4. The 4m and m2 -dimensional Nichols algebras B(Vabe) discovered first by Andruskiewitsch and Giraldi can be realized in the category of Yetter-Drinfeld modules over AµλNn. Using a result of Masuoka, we prove that dim B(Vabe) = ∞ under the condition b² = (ae)−1, b ∈ Gm for m ≥ 5. [ABSTRACT FROM AUTHOR]