Abstract

The purpose of this article is to provide a common framework for studying various generalizations of Leavitt path algebras. We first define Cohn-Leavitt path algebras of graphs with an additional structure called bi-separated graphs. We then define and study the category BSG of bi-separated graphs with appropriate morphisms so that the functor which associates bi-separated graphs to their Cohn-Leavitt path algebras is continuous. Next, we define two sub-categories of BSG, compute basis for the algebras corresponding to one of those subcategories and study some algebraic properties in terms of bi-separated graph-theoretic properties. Finally, we compute $\mathcal{V}$-monoid for some particular cases.

摘要

本文的目的是为研究Leavitt路径代数的各种泛化提供一个通用的框架。我们首先定义图的Cohn-Leavitt路径代数，并使用称为双分离图的附加结构。然后，我们定义并研究具有适当射影的双分离图的类别BSG，以便将双分离图与其Cohn-Leavitt路径代数关联的函子是连续的。接下来，我们定义BSG的两个子类别，为与这些子类别之一相对应的代数计算基础，并根据图分离的图论性质研究一些代数性质。最后，我们计算$\mathcal{伏特}$-monoid用于某些特定情况。