$C^*$-algebras associated to non-homogeneous minimal systems and their K-theory
$C^*$-algebras associated to non-homogeneous minimal systems and their K-theory
复制标题
与非齐次最小系统及其 K 理论相关的 $C^*$-代数
DOI：
10.7146/math.scand.a-13887
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发表时间：
1999
影响因子：
0.5
通讯作者：
Ø. Johansen
中科院分区：
文献类型：
--
作者：
Richard Gjerde;Ø. Johansen
Giordano，Putnam和Skau [4，定理2.1]证明了Cantor极小系统族的Krieger型定理成立，即（拓扑）轨道结构与相应的C -交叉积的同构类有关。很自然地，我们要研究一个类似的结果对于更大类的极小拓扑系统是否成立。假设Elliott猜想，即伴随的（简单）C -交叉积的完全同构不变量具有（有序）K-理论性质，考虑特殊的非齐次系统，给出了一个响亮的反例.我们提出的结构也有一个纯粹的动力学方面，这是独立的利益。如果我们将注意力限制在等度连续极小系统的非常特殊的族上，我们证明了Krieger型定理是真的，推广了Riedel [13]的一个结果。最后，我们研究了一般极小拓扑系统的强轨道等价的概念。在这方面，我们提出了一个相当令人惊讶的例子。
It has been proved by Giordano, Putnam and Skau [4, Theorem 2.1] that a Krieger type theorem holds for the family of Cantor minimal systems, i.e. the (topological) orbit structure is related to the isomorphism class of the associated C -crossed products. It is natural to investigate whether a similar result is true for a larger class of minimal topological systems. Assuming the Elliott conjecture, namely that a complete isomorphism invariant for the associated (simple) C -crossed products is of (ordered) K-theoretic nature, we give a resounding counterexample by considering special non-homogeneous systems. The construction we present also has a purely dynamical aspect, which is of independent interest. If we restrict attention to the very special family of equicontinuous minimal systems, we show that a Krieger type theorem is true, extending a previous result by Riedel [13]. Finally, we investigate the notion of strong orbit equivalence for minimal topological systems in general. We present a rather surprising example in this connection.