论文标题
lies nilpotent novikov代数，可解决的leavitt路径代数
Lie nilpotent Novikov algebras and Lie solvable Leavitt path algebras
论文作者
论文摘要
在本文中，我们首先研究了诺维科夫代数的下部链的特性。然后，我们证明，对于每个谎言，nilpotent novikov algebra〜 $ \ Mathcal {n} $，〜$ \ Mathcal {n} $的理想是由set〜 $ \ {ab -ba \ ba \ ba \ mid a，ba \ mid a，b \ in \ mathcal in \ nathcal {n} n} $ nillpotent。其次，我们在图$ e $和field $ k $上提供了必要和足够的条件，而Leavitt路径代数$ l_k（e）$可解决。因此，我们获得了lie nilpotent leavitt路径代数的完整描述，并表明〜$ l_k（e）$的谎言解决性和$ [l_k（e），l_k（e）] $的lie nilpotency是相同的。
In this paper, we first study properties of the lower central chains for Novikov algebras. Then we show that for every Lie nilpotent Novikov algebra~$\mathcal{N}$, the ideal of~$\mathcal{N}$ generated by the set~$\{ab - ba\mid a, b\in \mathcal{N}\}$ is nilpotent. We secondly provide necessary and sufficient conditions on the graph $E$ and the field $K$ for which the Leavitt path algebra $L_K(E)$ is Lie solvable. Consequently, we obtain a complete description of Lie nilpotent Leavitt path algebras, and show that the Lie solvability of~$L_K(E)$ and the Lie nilpotency of $[L_K(E),L_K(E)]$ are the same.
