论文标题
符号动力和矩阵的稳定代数
Symbolic dynamics and the stable algebra of matrices
论文作者
论文摘要
我们介绍了与符号动力学中某些问题有关的“矩阵稳定代数”。我们认为，对于一般环和各种特定环的矩阵，矩阵的稳定代数（尤其是移位等效性和强移等效）。该代数具有独立的兴趣，因此几乎不关注符号动态。我们包括牢固的连接，即代数K理论和非负矩阵的逆频谱问题。我们还回顾了有限类型的自动形态群体的关键特征，以及金，鲁西和瓦格纳的工作为威廉姆斯的班次等价猜想提供了反示例。
We give an introduction to the "stable algebra of matrices" as related to certain problems in symbolic dynamics. We consider this stable algebra (especially, shift equivalence and strong shift equivalence) for matrices over general rings as well as various specific rings. This algebra is of independent interest and can be followed with little attention to the symbolic dynamics. We include strong connectionsto algebraic K-theory and the inverse spectral problem for nonnegative matrices. We also review key features of the automorphism group of a shift of finite type, and the work of Kim, Roush and Wagoner giving counterexamples to Williams' Shift Equivalence Conjecture.
