论文标题
由Hausdorff的Steinberg代数产生的简单谎言代数
Simple Lie algebras arising from Steinberg algebras of Hausdorff ample groupoids
论文作者
论文摘要
在本文中，我们表明一个简单的Steinberg代数是中心的，而非家庭简单的Steinberg代数的中心为零。我们确定字段$ k $和hausdorff ample groupoids $ \ mathcal {g} $，简单的steinberg algebra $ a_k（\ mathcal {g}）$产生一个简单的lie elgebra $ [a_k（a_k（\ nathcal {g}）我们将获得的结果应用于简单的Leavitt路径代数，简单的Kumjian-pask代数和简单的Exel-Pardo代数来确定其相关的Lie代数很简单。特别是，我们提供了易于计算的标准，以确定表格$ [l_k（e），l_k（e）] $的代数为哪个代数，当$ e $是任意图形时，leavitt path algebra $ l_k（e）$很简单。同样，我们获得了Unital Simple Exel-Pardo代数是中心的，而非一个简单的Exel-Pardo代数为零中心。
In this paper, we show that a unital simple Steinberg algebra is central, and a nonunital simple Steinberg algebra has zero center. We identify the fields $K$ and Hausdorff ample groupoids $\mathcal{G}$ for which the simple Steinberg algebra $A_K(\mathcal{G})$ yields a simple Lie algebra $[A_K(\mathcal{G}), A_K(\mathcal{G})]$. We apply the obtained results on simple Leavitt path algebras, simple Kumjian-Pask algebras and simple Exel-Pardo algebras to determine their associated Lie algebras are simple. In particular, we give easily computable criteria to determine which Lie algebras of the form $[L_K(E), L_K(E)]$ are simple, when $E$ is an arbitrary graph and the Leavitt path algebra $L_K(E)$ is simple. Also, we obtain that unital simple Exel-Pardo algebras are central, and nonunital simple Exel-Pardo algebras have zero center.
