Diagrams of Hopf algebras with the Chevalley property  

作　　者：FAN Zhong-ping LU Di-ming YU Xiao-lan 

机构地区：[1]School of Mathematical Science, Ocean University of China [2]Department of Mathematics, Zhejiang University [3]Department of Mathematics, Hangzhou Normal University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2016年第3期367-378,共12页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11271319,11301126)

摘　　要：In this paper, we study non-cosemisimple Hopf algebras through their underlying coalgebra structure. We introduce the concept of the maximal pointed subcoalgebra/Hopf sub- algebra. For a non-cosemisimple Hopf algebra A with the Chevalley property, if its diagram is a Nichols algebra, then the diagram of its maximal pointed Hopf subalgebra is also a Nichols algebra. When A is of finite dimension, we provide a necessary and sufficient condition for A＇s diagram equaling the diagram of its maximal pointed Hopf subalgebra.In this paper, we study non-cosemisimple Hopf algebras through their underlying coalgebra structure. We introduce the concept of the maximal pointed subcoalgebra/Hopf sub- algebra. For a non-cosemisimple Hopf algebra A with the Chevalley property, if its diagram is a Nichols algebra, then the diagram of its maximal pointed Hopf subalgebra is also a Nichols algebra. When A is of finite dimension, we provide a necessary and sufficient condition for A＇s diagram equaling the diagram of its maximal pointed Hopf subalgebra.

关 键 词：Hopf algebra COALGEBRA coradical Nichols algebra pointed Chevalley property 

分 类 号：O153[理学—数学]