论文标题
在分级的Steinberg代数上的诱导分级简单模块上，应用于Leavitt Path代数
On induced graded simple modules over graded Steinberg algebras with applications to Leavitt path algebras
论文作者
论文摘要
对于$ \ Mathcal {g} $和一个单位的$ x $ $ \ Mathcal {g} $，Steinberg构建了模块类别之间的诱导和限制器，Steinberg algebra $ a_r（\ Mathcal {g}）$ and the Modules copt of is oft off the Isbropy offra构建了感应和限制器。 $ r \ Mathcal {g} _x $。在本文中，我们证明了这些函子的分级版本和相关的结果，用于分级的ampim glassoid的分级Steinberg代数。作为一个应用程序，对Leavitt路径代数$ L_K（E）$上的简单和分级的简单模块进行了分类。特别是，我们表明，许多先前已知的简单和分级的简单$ L_K（E）$ - 包括Chen Simple模块在内的模块，都是从（分级或非分级）的简单模块上诱导的，这些模块是各向同性组代数的简单模块。
For an ample groupoid $\mathcal{G}$ and a unit $x$ of $\mathcal{G}$, Steinberg constructed the induction and restriction functors between the category of modules over the Steinberg algebra $A_R(\mathcal{G})$ and the category of modules over the isotropy group algebra $R\mathcal{G}_x$. In this paper, we prove a graded version of these functors and related results for the graded Steinberg algebra of a graded ample groupoid. As an application, the spectral simple and graded simple modules over the Leavitt path algebra $L_K(E)$ are classified. In particular, we show that many of previously known simple and graded simple $L_K(E)$-modules, including the Chen simple modules, are induced from (graded or non-graded) simple modules over isotropy group algebras.
