STABLE RANK OF SOME CROSSED PRODUCT C -ALGEBRAS
STABLE RANK OF SOME CROSSED PRODUCT C -ALGEBRAS
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一些叉积C-代数的稳定秩
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
Y. Poon
中科院分区：
文献类型：
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作者：
Y. Poon
设C（X）xT Z是与动力系统（X，T）相关联的交叉积.给出了C（X）xT Z有可逆元稠密集的一个充要条件.当X为零维时，得到了C（X）xtZ的K-群与由X的T-不变闭子集定义的C*-代数同构的更多等价条件.作为一个应用，我们证明了这些条件不满足大多数子移位和所有非平凡不可约马尔可夫移位。当（X，T）不可分解时，一个等价条件是X的所有T-不变非空闭子集的交非空。
Let C(X) xT Z be the crossed product associated to a dynamical system (X , T). We give a necessary and sufficient condition for C(X) xT Z to have a dense set of invertible elements. When X is zero-dimensional, we obtain more equivalent conditions which involve the isomorphism between the K-groups of C{X)xtZ and C*-algebras defined by some T-invariant closed subsets of X. As an application, we show that these conditions are not satisfied by most subshifts and all nontrivial irreducible Markov shifts. When (X, T) is indecomposable, an equivalent condition is that the intersection of all T- invariant nonempty closed subsets of X is nonempty.