L-无穷代数作用
L-infinity algebra actions
摘要：
定义了L-无穷代数$g$在分次流形$M$上的作用的概念，并证明了这种作用对应于$g[1] \times M$上一个特定形式的同调向量场.这推广了流形上的李代数作用与变换李代数胚之间的对应关系。特别地，我们考虑了$g$在第二个L-无穷代数上的作用，从而得到了L-无穷代数的“半直积“的概念，比我们在文献中发现的更一般。
英文摘要：
We define the notion of action of an L-infinity algebra $g$ on a graded manifold $M$, and show that such an action corresponds to a homological vector field on $g[1] \times M$ of a specific form. This generalizes the correspondence between Lie algebra actions on manifolds and transformation Lie algebroids. In particular, we consider actions of $g$ on a second L-infinity algebra, leading to a notion of "semidirect product" of L-infinity algebras more general than those we found in the literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
