Leavitt路代数的扭曲何时再次成为Leavitt路代数
When twist of a Leavitt path algebra is again a Leavitt path algebra
- Institute of Mathematics, Vietnam Academy of Science and Technology（越南科学技术院数学研究所）
- Department of Mathematics and Statistics, Saint Louis University（圣路易斯大学数学与统计系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究Leavitt路代数在图自同构诱导的Zhang扭曲下何时仍为Leavitt路代数，建立了原图与扭曲图的组合联系，证明环论性质不变，并定义了Z-分次代数的非交换射影概形。
AI中文摘要：
本文研究了Leavitt路代数$L_K(E)$的Zhang扭曲，利用由图自同构诱导的分次自同构$\sigma$，使得扭曲后的代数是另一个图$E_{\sigma}$上的Leavitt路代数，其中$E_{\sigma}$是从原图$E$得到的扭曲图。我们建立了图$E$与$E_{\sigma}$之间的组合联系，并由此证明了在$\sigma$扭曲下，Leavitt路代数的许多环论性质保持不变。我们还定义了$\mathbb Z$-分次代数的非交换射影概形的概念，该概念与Artin和Zhang定义的连通$\mathbb N$-分次代数的非交换射影概形一致，并在Leavitt路代数扭曲的背景下对其进行了研究。
英文摘要：
In this paper, we study Zhang twist of Leavitt path algebra $L_K(E)$ using a graded automorphism $σ$ induced by a graph automorphism such that the twisted algebra is a Leavitt path algebra over another graph $E_σ$ which is a twisted graph obtained from the original graph $E$. We establish combinatorial connection between the graphs $E$ and $E_σ$ and as a consequence, we show that many ring-theoretic properties are invariant for Leavitt path algebras under the twist by $σ$. We also define the notion of noncommutative projective scheme for $\mathbb Z$-graded algebras that coincides with the notion of noncommutative projective scheme for connected $\mathbb N$-graded algebras defined by Artin and Zhang and study it in the context of twists of Leavitt path algebras.
