标题： 超自然矩阵的代数 显示英文标题

标题： The algebra of supernatural matrices

摘要： 超自然矩阵的代数是局部有限中心单代数理论中的一个关键例子，这一理论在作者之前的一篇论文（\cite{Local}）中有所研究。它也是一个独立的研究对象，具有丰富的研究内容和与其他领域的多种联系。 本文的目标是揭示关于超自然矩阵的一些新信息，主要集中在识别这类代数的“内在”方式上，并探讨它们作为形如$M_n(A)\cong A$方程的最小解出现的情况。 通过研究该代数的一个自然表示，我们证明了超自然矩阵同时推广了麦克里蒙深矩阵代数和$m$-花瓣李瓦特定向图代数。我们还研究了它们的简单表示。 显示英文摘要

摘要： The algebra of supernatural matrices is a key example in the theory of locally finite central simple algebras, which studied in a previous paper of the authors (\cite{Local}). It is also a stand-alone object admits a rich study and various connections to other fields. The goal of this paper is to expose some new information about supernatural matrices, mainly in terms of the "inner" ways to identify such algebras, and their appearance as minimal solutions to equations of the form $M_n(A)\cong A$. Viewing a natural representation of this algebra, we show that supernatural matrices generalize both McCrimmon's deep matrices algebra and $m$-petal Leavitt path algebra. We also study their simple representations.