Finite-dimensional Nichols algebras over the Suzuki algebras II: Simple Yetter–Drinfeld modules of AN2n+1μλ
-
Published:2023-05-11
Issue:
Volume:
Page:
-
ISSN:0219-4988
-
Container-title:Journal of Algebra and Its Applications
-
language:en
-
Short-container-title:J. Algebra Appl.
Affiliation:
1. Jiangxi Provincial Center for Applied Mathematics and School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi 330022, P. R. China
Abstract
In this paper, the author gives a complete set of simple Yetter–Drinfeld modules over the Suzuki algebra [Formula: see text] and investigates the Nichols algebras over those irreducible Yetter–Drinfeld modules. The finite-dimensional Nichols algebras of diagonal type are of Cartan type [Formula: see text], [Formula: see text], [Formula: see text], Super type [Formula: see text] and the Nichols algebra [Formula: see text]. And the involved finite-dimensional Nichols algebras of non-diagonal type are [Formula: see text], [Formula: see text] and [Formula: see text]-dimensional. The left three unsolved cases are set as open problems. In particular, all finite-dimensional Nichols algebras are given for simple Yetter–Dinfeld modules over [Formula: see text].
Funder
National Natural Science Foundation of China
Foundation of Jiangxi Educational Committee
Jiangxi Provincial Natural Science Foundation
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory