论文标题
纯粹无限的简单超级莱维特路径代数
Purely infinite simple ultragraph Leavitt path algebras
论文作者
论文摘要
在本文中，我们提供了必要和充分的条件，在此条件下，Leavitt路径代数$ l_k（\ Mathcal {g}）$ of Ultragraph $ \ MATHCAL {G} $上的字段$ k $纯粹是无限的简单，并且它是von Neumann的常规。因此，我们获得每个分级的简单超级莱维特路径代数是本地矩阵代数，或$ k [x，x^{ - 1}] $的完整矩阵环，或一个纯粹的无限简单代数。
In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $L_K(\mathcal{G})$ of an ultragraph $\mathcal{G}$ over a field $K$ is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over $K[x, x^{-1}]$, or a purely infinite simple algebra.
