| Gelfand-Naimark Theorem of Commutative Hopf C^＊ -Algebras |
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| 引用本文： | 刘明,蒋立宁. Gelfand-Naimark Theorem of Commutative Hopf C^＊ -Algebras[J]. 北京理工大学学报(英文版), 2006, 15(3): 374-378 |
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| 作者姓名： | 刘明 蒋立宁 |
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| 作者单位： | School of Science Beijing Institute of Technology Beijing 100081 China，School of Science Beijing Institute of Technology Beijing 100081 China |
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| 基金项目： | SponsoredbytheNationalNaturalScienceFoundationofChina(10301004)，ExcellentYoungScholarsResearchFundofBeijingInstituteofTechnology(000Y0725) |
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| 摘 要： | LetGbeacompactgroupwithaunitee,and C(G)thespaceofallcomplexcontinuousfunctions onG.C(G)isaC algebrawithproductdefined by(fg)(t)=f(t)g(t)andthestandardinvolution definedbyf(t)=f(t)(f,g∈C(G),t∈G).Underthestructuremaps(Δf)(s,t)=f(st),ε(f)=f(e)and(Sf)(t)=f(t-1),C(G)be comesaHopfalgebra.IfGisalocallycompact group,letC0(G)bethespaceofcomplexcontinuous functionsonGtendingto0atinfinity,C0(G)isal soaC algebra.HoweverC0(G)hasnounit,this leadstotheconceptofamultiplierHopfalgebra[1].Aswehave…
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| 关 键 词： | 可交换代数 Hopf C^＊代数 非退化性 Gelfand-Naimark定理 |
| 文章编号： | 1004-0579（2006）03-0374-05 |
| 收稿时间： | 2005-04-01 |
Gelfand-Naimark Theorem of Commutative Hopf C*-Algebras |
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| LIU Ming and JIANG Li-ning. Gelfand-Naimark Theorem of Commutative Hopf C*-Algebras[J]. Journal of Beijing Institute of Technology, 2006, 15(3): 374-378 |
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| Authors: | LIU Ming and JIANG Li-ning |
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| Affiliation: | School of Science, Beijing Institute of Technology, Beijing 100081, China;School of Science, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | Let A be a commutative C* -algebra. By the Gelfand-Naimark theorem, there exists a locally compact space G such that A is isomorphic to C0(G), the C* -algebra of all complex continuous functions on G vanishing at infinity. The result is generalized to the case of Hopf C* -algebra, where G is altered by a locally compact group. Using the isomorphic representation, the counit ε and the antipode S of a commutative Hopf C* -algebra are proposed. |
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| Keywords: | Hopf C*-algebra representation non-degenerate |
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