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On the Green rings of finite dimensional Hopf algebras
Zhihua Wang 1, 1, Yin-huo Zhang 2
1. Z. Wang ewline School of Mathematical Science, Yangzhou University, Yangzhou 225002, China
2. Y. H. Zhang ewline Department of Mathematics and Statistics, University of Hasselt, Universitaire Campus, 3590 Diepeenbeek, Belgium
*Correspondence author
#Submitted by
Subject:
Funding: Ph. D. Programs Foundation of Higher Education of China （No.20123250110005）
Opened online: 7 June 2016
Accepted by: none
Citation: Zhihua Wang,, Yin-huo Zhang.On the Green rings of finite dimensional Hopf algebras[OL]. [ 7 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4693663
 
 
When $H$ is an arbitrary finite dimensional Hopf algebra over an algebraically closed field, we character whether or not the trivial module appears as a direct summand of the tensor product for any two indecomposable modules. We use these characterizations to obtain some one-sided ideals of the Green ring of Hopf algebra $H$. This allows us to study the nilpotent radical and central primitive idempotents of the Green ring. We study the Green ring of $H$ by virtue of bilinear forms. If $H$ is of finite representation type, the Green ring is a Frobenius algebra over $mathbb{Z}$ with the dual basis associated to almost split sequences.
Keywords:Green ring, bilinear form, finite representation type, bi-Frobenius algebra
 
 
 

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