论文标题
强烈分级的Leavitt路径代数
Strongly graded Leavitt path algebras
论文作者
论文摘要
令$ r $为一个Unital环，让$ e $为有名图表，并回想一下Leavitt Path代数$ l_r（e）$带有天然$ \ Mathbb {z} $ - 等级。我们表明，$ l_r（e）$是强烈的$ \ mathbb {z} $ - 当且仅当$ e $是行列，没有下沉，没有下沉，并且满足条件（y）时。我们的结果概括了克拉克，哈兹拉特和里格比的最新结果，证明是简短而独立的。
Let $R$ be a unital ring, let $E$ be a directed graph and recall that the Leavitt path algebra $L_R(E)$ carries a natural $\mathbb{Z}$-gradation. We show that $L_R(E)$ is strongly $\mathbb{Z}$-graded if and only if $E$ is row-finite, has no sink, and satisfies Condition (Y). Our result generalizes a recent result by Clark, Hazrat and Rigby, and the proof is short and self-contained.
