| Generalized Path Algebras and Pointed Hopf Algebras |
| Received:January 21, 2007 Revised:July 13, 2008 |
| Key Words:
generalized path algebra Hopf algebra radical.
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| Fund Project: |
| Author Name | Affiliation | | ZHANG Shou Chuan | Department of Mathematics, Hunan University, Hunan 410082, China
Department of Mathematics, University of Queensland, Brisbane 4072, Australia
The Center of Combinatorial Mathematics, Nankai University, Tianjin 300071, China | | ZHANG Yao Zhong | Department of Mathematics, University of Queensland, Brisbane 4072, Australia | | GUO Xi Jing | Department of Mathematics, Zhuhai College of Jilin University, Guangdong 519041, China |
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| Abstract: |
| Most of pointed Hopf algebras of dimension $p^m$ with large coradical are shown to be generalized path algebras. By the theory of generalized path algebras, the representations, homological dimensions and radicals of these Hopf algebras are obtained. The relations between the radicals of path algebras and connectivity of directed graphs are given. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.03.003 |
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