论文标题
关于代数组移动的动态有限性能
On dynamical finiteness properties of algebraic group shifts
论文作者
论文摘要
让$ g $为一个组，让$ v $是代数封闭的字段的代数组。我们介绍了代数组子缩影$σ\ subset v^g $，它概括了$ v^g $的代数Sofic sofic subshifts of $ v^g $的类别，以及对有限组字母的封闭组subshifts等级。当$ g $是逐限的一组时，我们表明$ v^g $满足了降链条件，并且代数组子缩影的概念，代数组的SOFIC子缩影的概念，以及代数的代数组群的概念，对有限的有限型组均等。因此，我们获得了厨房和施密特的众所周知结果的扩展，以涵盖许多非压缩组字母的情况。
Let $G$ be a group and let $V$ be an algebraic group over an algebraically closed field. We introduce algebraic group subshifts $Σ\subset V^G$ which generalize both the class of algebraic sofic subshifts of $V^G$ and the class of closed group subshifts over finite group alphabets. When $G$ is a polycyclic-by-finite group, we show that $V^G$ satisfies the descending chain condition and that the notion of algebraic group subshifts, the notion of algebraic group sofic subshifts, and that of algebraic group subshifts of finite type are all equivalent. Thus, we obtain extensions of well-known results of Kitchens and Schmidt to cover the case of many non-compact group alphabets.
