论文标题
有针对性图的才华横溢的单体，并应用了代数图形
The talented monoid of a directed graph with applications to graph algebras
论文作者
论文摘要
这是一个猜想的是，对于有限的定向图的Leavitt路径代数的类别，其分级的Grothendieck组$ K_0^{\ Mathrm {gr}} $是一个完整的不变性。对于Leavitt Path PATH代数$ l _ {\ Mathsf K}（E）$，在字段中具有系数$ {\ Mathsf K} $，$ K_0^{\ Mathrm {grmmatrm {Grm {gr}}}的正锥的单体（L _ {\ Mathsf K}（e）$均可用$ E.在本说明中，我们进一步研究了这种“才华横溢的单体”的结构，显示了它如何捕获图形的内在特性，从而捕获了相关的Leavitt路径代数的结构。特别是，对于紧密连接的图表，我们表明，可以通过才华横溢的单体完全描述图表的概念。作为应用程序，我们将根据相关图的性质对纯粹的无限简单LEAVITT路径代数的表征进行更精细的表征。我们表明，代数的分级同构保留了图的周期，并获得结果为分级分类的猜想提供了更多证据。
It is a conjecture that for the class of Leavitt path algebras associated to finite directed graphs, their graded Grothendieck groups $K_0^{\mathrm{gr}}$ are a complete invariant. For a Leavitt path algebra $L_{\mathsf k}(E)$, with coefficient in a field ${\mathsf k}$, the monoid of the positive cone of $K_0^{\mathrm{gr}}(L_{\mathsf k}(E))$ can be described completely in terms of the graph $E$. In this note we further investigate the structure of this "talented monoid", showing how it captures intrinsic properties of the graph and hence the structure of its associated Leavitt path algebras. In particular, for the class of strongly connected graphs, we show that the notion of the period of a graph can be completely described via the talented monoid. As an application, we will give a finer characterisation of the purely infinite simple Leavitt path algebras in terms of properties of the associated graph. We show that graded isomorphism of algebras preserve the period of the graphs, and obtain results giving more evidence to the graded classification conjecture.
