论文标题
加权和分离图的Leavitt路径代数
Leavitt path algebras of weighted and separated graphs
论文作者
论文摘要
在本文中，我们表明，加权图的Leavitt路径代数和分离图的Leavitt路径代数密切相关。我们证明，排行线顶点加权图$（e，ω）$的任何Leavitt Path emgra $ l（e，ω）$ is $*$ - 同构对特定双部分分离的图形$（e（ω），c（ω））$的下列莱维特路径代数。 For a general locally finite weighted graph $(E, ω)$, we show that a certain quotient $L_1(E,ω)$ of $L(E,ω)$ is $*$-isomorphic to an upper Leavitt path algebra of another bipartite separated graph $(E(w)_1,C(w)^1)$.我们还介绍了代数$ l^{\ mathrm {ab}}（e，w）$，这是由一组部分异构体生成的通用驯服$*$ - 代数。我们为$ l（e，ω）$的理想结构带来了一些结果，我们详细研究了Leavitt代数$ L（m，n）$的两种不同的最大理想。
In this paper we show that Leavitt path algebras of weighted graphs and Leavitt path algebras of separated graphs are intimately related. We prove that any Leavitt path algebra $L(E,ω)$ of a row-finite vertex weighted graph $(E,ω)$ is $*$-isomorphic to the lower Leavitt path algebra of a certain bipartite separated graph $(E(ω),C(ω))$. For a general locally finite weighted graph $(E, ω)$, we show that a certain quotient $L_1(E,ω)$ of $L(E,ω)$ is $*$-isomorphic to an upper Leavitt path algebra of another bipartite separated graph $(E(w)_1,C(w)^1)$. We furthermore introduce the algebra $L^{\mathrm{ab}} (E,w)$, which is a universal tame $*$-algebra generated by a set of partial isometries. We draw some consequences of our results for the structure of ideals of $L(E,ω)$, and we study in detail two different maximal ideals of the Leavitt algebra $L(m,n)$.
