| 引用本文： |
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赵汝菊,任北上,夏嘉艺,江妙浩.群像余代数的结构研究[J].广西科学,2015,22(2):228-230,236. [点击复制]
- ZHAO Ru-ju,REN Bei-shang,XIA Jia-yi,JIANG Miao-hao.Structures of Grouplike Coalgebras[J].Guangxi Sciences,2015,22(2):228-230,236. [点击复制]
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| 摘要: |
| 研究群像余代数K[S]和K[G]的结构,其中S是一个非空集合,G是一个只有单位元和逆元的幺半群,得到结论:对任意g∈G,g'∈G',定义f'(g,g')=g⊗g',则线性同构k[G×G']≃k[G]⊗k[G']是余代数同构. |
| 关键词: 群像余代数 张量积 余代数同构 |
| DOI：10.13656/j.cnki.gxkx.20140610.003 |
| 投稿时间：2014-04-05修订日期：2014-09-21 |
| 基金项目:广西自然科学基金项目(2011GXNSFA018144),2012年度新世纪广西高等教育教学改革工程立项项目(2012JGA162)和广西研究生教育创新计划项目(JGY2014092)资助。 |
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| Structures of Grouplike Coalgebras |
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ZHAO Ru-ju, REN Bei-shang, XIA Jia-yi, JIANG Miao-hao
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| (College of Mathematicas and Statistics Sciences, Guangxi Teachers'Education University, Nanning, Guangxi, 530023, China) |
| Abstract: |
| In this paper, we investigate the sructures of grouplike coalgebras K[S] and K[G], where S is a non-empty set and G is a monoid whose identity e is the only invertible element of G, and obtain the conclusion that the K-linear isomorphism K[G×G']≃K[G]⊗K[G'] defined by f'(g, g')=g⊗g', for all g∈G, g'∈G' is an isomorphism of coalgebra. |
| Key words: grouplike coalgebra tensor product isomorphism of coalgebra |
