超几何形式中的Jacobi结构
Jacobi structures in supergeometric formalism
摘要：
我们使用超几何形式主义，更准确地说，所谓的“大括号”（括号和锚是由一些分次辛流形上的函数编码），以解决Jacobi代数胚和双代数胚的理论（以下主要是伊格莱西亚斯-马雷罗和Grabowski-Marmo作为指导方针）。这种形式主义是特别有效的定义Jacobi-Gerstenhaber代数结构相关联的Jacobi代数体，定义其泊松化，并表示相容性条件定义Jacobi双代数体。此外，我们声称，这种超几何语言给出了一个简单的描述的Jacobi bialgebroid与Jacobi结构，相反，Jacobi结构与Jacobi bialgebroid。
英文摘要：
We use the supergeometric formalism, more precisely, the so-called "big bracket" (for which brackets and anchors are encoded by functions on some graded symplectic manifold) to address the theory of Jacobi algebroids and bialgebroids (following mainly Iglesias-Marrero and Grabowski-Marmo as a guideline). This formalism is in particular efficient to define the Jacobi-Gerstenhaber algebra structure associated to a Jacobi algebroid, to define its Poissonization, and to express the compatibility condition defining Jacobi bialgebroids. Also, we claim that this supergeometric language gives a simple description of the Jacobi bialgebroid associated to Jacobi structures, and conversely, of the Jacobi structure associated to Jacobi bialgebroid.
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。
