| 可能行无限图C~*-代数 |
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| 引用本文： | 方小春,成荣,邱伯驺.可能行无限图C~*-代数[J].数学学报,2004,47(4):687-694. |
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| 作者姓名： | 方小春 成荣 邱伯驺 |
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| 作者单位： | 同济大学应用数学系,上海,200092 |
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| 基金项目： | 国家自然科学基金(10271090) |
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| 摘 要： | 本文研究可能行无限有向图的C~*-代数。对于一个可能行无限的有向图E,通过引进集合S(μ,v),将行无限点上的算子拓扑强收敛关系代数化表示出来,并由此构造了一个结构丰富的非零*-代数H_E;进而利用H_E证明了一个由Cuntz-Krieger E-族{s_e,p_v}生成的泛C~*-代数 C~*(E)的存在性,并且证明了H_E和 C~*(E)在图同构意义下不依赖于E的选择,从而是可能行无限有向图的同构不变量。
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| 关 键 词： | Cuntz-Krieger E-族 可能行无限的有向图 图代数 |
| 文章编号： | 0583-1431(2004)04-0687-08 |
The C~*-Algebras of Possibly Row-Infinite Directed Graphs |
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| Xiao Chun FANG,Rong CHENG,Bo Zou QIU.The C~*-Algebras of Possibly Row-Infinite Directed Graphs[J].Acta Mathematica Sinica,2004,47(4):687-694. |
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| Authors: | Xiao Chun FANG Rong CHENG Bo Zou QIU |
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| Affiliation: | Xiao Chun FANG;Rong CHENG;Bo Zou QIU Department of Applied Mathematics,Tongji University,Shanghai 200092, P. R. China |
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| Abstract: | This paper is about the C~*-algebras of possibly row-infinite directed graphs.
For a possibly row-infinite directed graph E, we introduce the set s(μ,ν), by which
the strong operator topology on the row-infinite vertices is algebraically represented.
Moreover, a *-algebra H_E with rich structure is constructed, by which the existence of
the universal C~*-algebra generated by Cuntz-Krieger E-family {s_e, p_ν} is proved. We
also proved that the H_E and C~*(E) are the isomorphism invariants of E. |
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| Keywords: | Cuotz-Krieger E-family Possibly row-infinite directed graphs Graph algebras |
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