论文标题
图类别的流量等效性和Leavitt路径代数
Flow equivalence of diagram categories and Leavitt path algebras
论文作者
论文摘要
众所周知，源自符号动力学流动等效性研究的有导向图的几种结构已知，以保留Leavitt Path代数的Morita等效类别的莫里塔等效等级。我们通过对这些等价定理的制定和证明概括来做到这一点，在这些定理中，F-Vector空间的类别被带有二进制共同体的任意类别取代，表明Morita等效性结果的结果仅取决于形成向量空间的直接成本的能力。我们建议本文开发的框架可能有助于研究与Leavitt Path代数相关性有关的其他问题。
Several constructions on directed graphs originating in the study of flow equivalence in symbolic dynamics (e.g., splittings and delays) are known to preserve the Morita equivalence class of Leavitt path algebras over any coefficient field F. We prove that many of these equivalence results are not only independent of F, but are largely independent of linear algebra altogether. We do this by formulating and proving generalisations of these equivalence theorems in which the category of F-vector spaces is replaced by an arbitrary category with binary coproducts, showing that the Morita equivalence results for Leavitt path algebras depend only on the ability to form direct sums of vector spaces. We suggest that the framework developed in this paper may be useful in studying other problems related to Morita equivalence of Leavitt path algebras.
