交叉积中的动力系统与交换子
Dynamical Systems and Commutants in Crossed Products
AI总结：
本文研究函数代数子代数在与整数构成的交叉积中的交换子，给出其极大交换的充要条件，并将其转化为拓扑动力学条件，进而推广到交换完全正则半单 Banach 代数。
摘要：
本文描述了集合 $X$ 上函数代数 $A$ 的任意子代数在 $A$ 与整数构成的交叉积中的交换子，其中整数通过由 $X$ 的一个双射定义的复合自同构作用于 $A$。由此得到的关于 $A$ 在交叉积中为极大交换的充分必要条件，随后被应用于这些条件可被证明等价于拓扑动力学中某一条件的情形。进一步地，利用 Gelfand 变换，我们针对交换的完全正则半单 Banach 代数，在其特征空间上得到一个拓扑动力学条件，该条件等价于该代数在与整数构成的交叉积中为极大交换。
英文摘要：
In this paper we describe the commutant of an arbitrary subalgebra $A$ of the algebra of functions on a set $X$ in a crossed product of $A$ with the integers, where the latter act on $A$ by a composition automorphism defined via a bijection of $X$. The resulting conditions which are necessary and sufficient for $A$ to be maximal abelian in the crossed product are subsequently applied to situations where these conditions can be shown to be equivalent to a condition in topological dynamics. As a further step, using the Gelfand transform we obtain for a commutative completely regular semi-simple Banach algebra a topological dynamical condition on its character space which is equivalent to the algebra being maximal abelian in a crossed product with the integers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
