Courant代数胚与广义复几何

Courant algebroids and generalized complex geometry

本文综述Courant代数胚的研究背景、发展历史、重要理论及其应用.本文回顾和介绍该领域中一些关键的发现和进展,并重点阐述Courant代数胚定义的来龙去脉,以及相应的Dirac结构、李双代数胚、Clifford构造、旋量表示、广义复几何以及正则Courant代数胚的理论框架和一些主要的结论.

In this survey, we recall the background and major developments in Courant algebroids and their applications. We mainly recall the origin and motivation of the definition of Courant algebroids. A brief introduction to the theories of Dirac structures, Lie bialgebroids, the Clifford construction, spinor representation,generalized complex geometry and regular Courant algebroids are given.