广义复结构在$\mathcal{G}$-平坦传递Courant代数胚上的形变
Deformations of generalized complex structures on $\mathcal{G}$-flat transitive Courant algebroids
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中文总结 AI 辅助
本文将广义复结构形变定理从精确Courant代数胚推广至$\mathcal{G}$-平坦传递情形，利用驯服Fréchet空间与Nash-Moser定理，并构造了具有驯服李群结构的自等价群及其精确子群。
中文摘要 AI 辅助
我们将Gualtieri关于精确Courant代数胚上广义复结构的形变定理推广到更一般的$\mathcal{G}$-平坦传递Courant代数胚类。我们的方法依赖于驯服Fréchet空间框架和Hamilton的Nash-Moser（隐函数）定理。作为我们形变定理证明的重要一步，我们赋予$\mathcal{G}$-平坦传递Courant代数胚的自等价群以驯服Fréchet李群结构，并证明存在一个精确自等价的驯服子群，其无穷小作用由内导子给出。
英文摘要
We extend Gualtieri's deformation theorem for generalized complex structures on exact Courant algebroids to the more general class of $\mathcal{G}$-flat transitive Courant algebroids. Our approach relies on the framework of tame Fréchet spaces and Hamilton's Nash-Moser (implicit function) theorem. As an important step of the proof of our deformation theorem, we endow the group of autoequivalences of a $\mathcal{G}$-flat transitive Courant algebroid with a tame Fréchet Lie group structure and show that there exists a tame subgroup of exact autoequivalences, whose infinitesimal action is by inner derivations.
