伽利略共形代数的双导子和线性交换映射
Biderivations and Linear CommutingMaps on the Galilean Conformal Algebra
摘要: 本文研究了(d + 1)维时空中的伽利略共形代数的反对称双导子和线性交换映射。首先证明了该代数上的所有反对称双导子都是内双导子；作为应用，我们确定了一类包含该代数在内的李代数L上的任一线性交换映射σ都具有如下形式: 对任意的x ∈ L，σ(x) = αx，α ∈ ℂ。且该类代数包含了平面伽利略共形代数。
Abstract: In this paper, we study skew-symmetric biderivations and linear commuting maps of the Galilean conformal algebra in (d + 1)-dimensional space-time. We first prove that each skew-symmetric biderivation of this algebra is inner. As an application of biderivations, we show that every linear commuting map σ on a certain class of Lie algebra L containing this algebra is of the form σ(x) = αx for all x ∈ L, where α ∈ ℂ. This class of Lie algebras includes the planar Galilean conformal algebra.
文章引用：王国泰, 申冉. 伽利略共形代数的双导子和线性交换映射[J]. 理论数学, 2026, 16(7): 72-85. https://doi.org/10.12677/PM.2026.167174

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