论文标题
subshift的海市rage楼的karoubi信封
The Karoubi envelope of the mirage of a subshift
论文作者
论文摘要
我们研究了与$ a^{\ Mathbb z} $的每个子缩影$ \ Mathcal x $相关的信件，该子类别是由$ a $生成的免费Profinite Semigroup的Karubi信封的子类别。该类别的对象是$ \ Mathcal x $的幻影中的dempotents，也就是说，在伪造的集合中，其有限因子是$ \ Mathcal x $的块。该类别的自然当量类别在流量等效性下被证明是不变的。作为我们证明的必然性，我们推断出与每个不可减至的子移位相关的涂鸦群的流动不变性。我们还以功能的方式表明，该类别的同构类别在共轭中是不变的。最后，我们看到$ \ Mathcal X $的Zeta函数自然编码在类别中。这些结果具有明显的翻译，可以在许多假娃娃群上进行相对免费的涂鸦半群，包括所有$ \ overline {\ mathsf h} $的所有形式，$ \ mathsf h $ a pseudovariety os pseudovariety。
We study a correspondence associating to each subshift $\mathcal X$ of $A^{\mathbb Z}$ a subcategory of the Karoubi envelope of the free profinite semigroup generated by $A$. The objects of this category are the idempotents in the mirage of $\mathcal X$, that is, in the set of pseudowords whose finite factors are blocks of $\mathcal X$. The natural equivalence class of the category is shown to be invariant under flow equivalence. As a corollary of our proof, we deduce the flow invariance of the profinite group that Almeida associated to each irreducible subshift. We also show, in a functorial manner, that the isomorphism class of the category is invariant under conjugacy. Finally, we see that the zeta function of $\mathcal X$ is naturally encoded in the category. These results hold, with obvious translations, for relatively free profinite semigroups over many pseudovarieties, including all of the form $\overline{\mathsf H}$, with $\mathsf H$ a pseudovariety of groups.
