发表机构
University of Colorado, Colorado Springs; Università degli Studi di Verona; Università degli Studi di Padova（科罗拉多大学斯普林斯分校; 维罗纳大学; 帕多瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画莱维特路代数单左理想，显式构造其内射包络，将雅可比代数相关构造推广至所有图的所有单左理想，还给出两类无限发射点对应单模内射包络的描述。
AI 中文摘要
设K为任意域，E为任意有向图。我们对莱维特路代数$L_K(E)$的单（即极小）左理想给出同构意义下的刻画。随后，对$L_K(E)$的每个单（即极小）左理想I，我们显式构造I的内射包络。该结果将三位作者此前针对雅可比代数$R=K\big\braket{X,Y \bigm| XY=1}$及单左R-理想$R(1-YX)$的特殊情形给出的构造，推广至所有图E和$L_K(E)$的所有单左理想。我们的方法涉及在无限级数的K-向量空间上定义$L_K(E)$-模结构。文末我们展示，该构造如何直接给出由E中两类无限发射点产生的单$L_K(E)$-模的内射包络的描述。
英文摘要
Let $K$ be any field and $E$ any directed graph. We characterize up to isomorphism the simple (i.e., minimal) left ideals of the Leavitt path algebra $L_K(E)$. Then, for each simple %(i.e., minimal) left ideal $I$ of %the Leavitt path algebra $L_K(E)$, we explicitly construct the injective envelope of $I$. This result generalizes to all graphs $E$ and all simple left ideals in $L_K(E)$ the construction presented previously by the three authors for the specific case of the Jacobson algebra $R=K\langle X,Y | XY=1\rangle$ and the simple left $R$-ideal $R(1-YX)$. Our method involves defining an $L_K(E)$-module structure on a $K$-vector space of infinite series. We conclude the article by showing how our construction directly gives a description of the injective envelope of simple $L_K(E)$-modules arising from two types of infinite emitters in $E$.
