论文标题
通过Serre属性区分有限图的Leavitt代数
Distinguishing Leavitt algebras among Leavitt path algebras of finite graphs by Serre property
论文作者
论文摘要
Leavitt Path path代数的核心中的两个未解决的问题是Grothendieck $ k_0 $是否是一个完全不变的，对于Unital纯无限的简单代数和一个较弱的问题，是否是$ l_2 $（是否与leavitt path algebra与Two loop looptex相关的Leavitt path algebra and two looptexs）和is is is is is iss $ easbra $ ___________________第一个问题的积极答案意味着后者。在这篇简短的论文中，我们提出并调查了另一个问题，即所谓的Serre的猜想，该猜想位于以上两个问题之间：分类问题的积极答案意味着Serre的猜想又意味着$ L_2 \ cong l_ cong l_ {2-} $。一路上，我们提供了新的易于构建的代数，具有稳定但不是免费模块的稳定的代数。
Two unanswered questions in the heart of the theory of Leavitt path algebras are whether Grothendieck group $K_0$ is a complete invariant for the class of unital purely infinite simple algebras and, a weaker question, whether $L_2$ (the Leavitt path algebra associated to a vertex with two loops) and its Cuntz splice algebra $L_{2-}$ are isomorphic. The positive answer to the first question implies the latter. In this short paper, we raise and investigate another question, the so-called Serre's conjecture, which sits in between of the above two questions: The positive answer to the classification question implies Serre's conjecture which in turn implies $L_2 \cong L_{2-}$. Along the way, we give new easy to construct algebras having stable free but not free modules.
