Smale空间上的广群C^＊—代数的迹  

ON THE TRACES OF THE GROUPOID C*-ALGEBRAS FROM SMALE SPACES

作　　者：侯成军[1] 

机构地区：[1]曲阜师范大学数学系

出　　处：《数学年刊（A辑）》2003年第2期137-144,共8页Chinese Annals of Mathematics

基　　金：国家青年基金(No.10201007)资助的项目.

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.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.

关 键 词：Smale空间 广群C^＊-代数 Ruelle代数 迹 

分 类 号：O177.5[理学—数学]