发表机构
Center for University Mathematics Teaching, College of Science, Nanjing Forestry University; Department of Mathematics, College of Mathematics and Physics, Beijing University of Chemical Technology（南京林业大学理学院; 北京化工大学数理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对单项式群相关的超平面排列，提出结合分隔子与积分表达式的构造方法，证明当p<r时导子模由标准导子及有限分隔子导子生成，推广了完全图情形。
AI 中文摘要
我们研究了与单项式群 $G(r,p,\ell)$ 相关的超平面排列的导子模。受 Mühlherr 基于分隔子的图排列构造方法的启发，我们将分隔子与积分表达式相结合，扩展了该方法。对于由图 $G$ 定义的子排列 $\mathcal{A}_G$，我们证明当 $p<r$ 时，导子模 $\mathcal{D}(\mathcal{A}_G)$ 由标准导子 $\eta_0,\dots,\eta_{\kappa(G)}$ 以及一组有限的基于分隔子的导子生成。该结果推广了完全图情形，并为分隔子方法在超平面排列研究中的更广泛应用提供了新的证据。
英文摘要
We investigate derivation modules of hyperplane arrangements associated with the monomial groups $G(r,p,\ell)$. Motivated by Mühlherr's separator-based construction for graphic arrangements, we extend this approach by combining separators with integral expressions. For a subarrangement $\mathcal{A}_G$ defined by a graph $G$, we show that, when $p<r$, the derivation module $\mathcal{D}(\mathcal{A}_G)$ is generated by the standard derivations $η_0,\dots,η_{κ(G)}$ together with a finite set of separator-based derivations. This result generalizes the complete graph case and provides new evidence toward the broader applicability of separator methods in the study of hyperplane arrangements.
Comments17 pages
