论文标题
实现Ultragraph Leavitt路径代数为Steinberg代数
Realizing ultragraph Leavitt path algebras as Steinberg algebras
论文作者
论文摘要
在本文中，我们将Leavitt Path代数为Steinberg代数。这种实现使我们能够使用群体素的方法来获得有关这些代数的结构结果。使用偏斜的乘积类固醇，我们表明Leavitt Path代数为von Neumann常规环。我们表征了强烈分级的Ultragraph Leavitt Path代数，并表明每个Ultragraph Leavitt Path eargebra代数都是半i富度的。此外，我们表征了Ultragraph Leavitt Path代数的不可还原表示。我们还表明，Leavitt路径代数可以实现为Cuntz-Pimsner环。
In this article, we realize ultragraph Leavitt path algebras as Steinberg algebras. This realization allows us to use the groupoid approach to obtain structural results about these algebras. Using skew product groupoid, we show that ultragraph Leavitt path algebras are graded von Neumann regular rings. We characterize strongly graded ultragraph Leavitt path algebras and show that every ultragraph Leavitt path algebra is semiprimitive. Moreover, we characterize irreducible representations of ultragraph Leavitt path algebras. We also show that ultragraph Leavitt path algebras can be realized as Cuntz-Pimsner rings.
