发表机构
National University of Uzbekistan named after Mirzo Ulugbek; Urgench State University; V.˜I.˜Romanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan（乌兹别克斯坦国立大学（米佐·乌鲁格别克命名）; Urgench州立大学; 乌兹别克斯坦科学院 V.I.罗曼诺夫斯基数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文统一研究了共形伽利略代数在三种中心扩张情形下的局部导子，确定了其结构，并解决了代数自反性问题，揭示了质量中心扩张消除额外局部自由度的关键作用。
AI 中文摘要
我们在三种自然情形下对共形伽利略李代数上的局部导子进行了统一研究：无中心扩张的代数、质量中心扩张以及奇异中心扩张。我们首先确定了导子代数的结构形式，并分离出相关的外导子。对于质量扩张，我们通过直接计算，在先前一维处理未覆盖的两个低参数处完成了一串刚性，并结合新的空间相容性论证，在任意空间维度上得到了结果。奇异扩张则通过其定义关系的自包含论证来处理。对于无中心扩张的代数，我们完全解决了剩余的代数自反性问题。若$d\ge2$，每个局部导子都是导子。在空间维度$d=1$时，当$2\ell$为偶数以及$\ell=\frac12$时，同样的结论成立；然而，对于奇数$2\ell\ge3$，存在额外的$(2\ell-1)$维纯局部导子空间。这与质量中心扩张形成鲜明对比，在质量中心扩张中，中心的Heisenberg配对恰好消除了这一额外的局部自由度。我们还确定了完整局部导子空间的李代数结构：在例外的一维非中心情形中，它是一个显式的半直积，带有一个额外的阿贝尔不可约理想。
英文摘要
We give a unified study of local derivations on conformal Galilei Lie algebras in three natural settings: the algebra without central extension, the mass central extension, and the exotic central extension. We first determine the structural form of the derivation algebras and isolate the relevant outer derivations. For the mass extension, we complete the one-string rigidity at the two low parameters not covered by the previous one-dimensional treatment, using direct calculations, and combine this with new spatial compatibility arguments to obtain the result in arbitrary spatial dimension. The exotic extension is treated by a self-contained argument from its defining relations. For the algebra without central extension we resolve the remaining algebraic-reflexivity problem completely. If $d\ge2$, every local derivation is again a derivation. In spatial dimension $d=1$, the same conclusion holds when $2\ell$ is even and also for $\ell=\frac12$; however, for odd $2\ell\ge3$ there is an additional $(2\ell-1)$-dimensional space of pure local derivations. This gives a sharp contrast with the mass central extension, where the central Heisenberg pairing removes precisely this extra local freedom. We also determine the Lie algebra structure of the full local-derivation space: in the exceptional one-dimensional non-central case it is an explicit semidirect product with an additional abelian irreducible ideal.
