| Smale空间上的广群C~*-代数的迹 |
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| 引用本文： | 侯成军.Smale空间上的广群C~*-代数的迹[J].数学年刊A辑(中文版),2003(2). |
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| 作者姓名： | 侯成军 |
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| 作者单位： | 曲阜师范大学数学系 山东曲阜273165 |
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| 基金项目： | 国家青年基金(No.10201007)资助的项目. |
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| 摘 要： | 本文证明由拓扑混合的Smale空间上的渐进等价关系定义的广群C*-代数及其相应的Ruelle代数有唯一的迹态;在拓扑可迁的情形下,证明此C*-代数的迹态构成了一个单形,此单形顶点的个数等于“Smale谱分解”中基本空间的个数,单形的重心是该C*-代数的唯一的αa-不变迹态;此回答了I.Putnam的一个猜测.
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| 关 键 词： | Smale空间 广群C*-代数 Ruelle代数 迹 |
ON THE TRACES OF THE GROUPOID C~*-ALGEBRAS FROM SMALE SPACES |
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| HOU Chengjun.ON THE TRACES OF THE GROUPOID C~*-ALGEBRAS FROM SMALE SPACES[J].Chinese Annals of Mathematics,2003(2). |
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| Authors: | HOU Chengjun |
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| Institution: | HOU Chengjun
Department of Mathematics,Qufu Normal University,Shandong Qufu 273165,China. Institute of Mathematics,Fudan University,Shanghai 200433,China. Institute of Mathematics,Chinese Academy of Science,Beijing 100080,China. E-mail: chjhou@etang.com |
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| Abstract: | We show that the groupoid C*-algebra, constructed from the asymptotic equivalence relation on the points of an irreducible Smale space, and the related Ruelle algebra has unique tracial state, respectively; we also show that when the Smale space is topological transitive, all the tracial states of the groupoid C*-algebra form a simplex with number of vertices equal to that of the base spaces in the "Smale's Spectral Decomposition". Moreover, the barycenter of the simplex is an a-invariant tracial state which is unique. |
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| Keywords: | Smale space Groupoid C*-algebra Trace |
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