Van Est integration in higher Lie theory

Van Est 融入高李理论

• 批准号: 446784784
• 负责人: Professorin Dr. Madeleine Jotz
• 金额: --
• 依托单位: Mathematisches Institut (MI)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/446784784?language=en
• 关键词: Van; Est; integration; higher; Lie

Lie algebroids and their higher version the Lie $n$-algebroids are differential graded manifolds and they describe infinitesimal symmetries. The integration of these structures to structures encoding global symmetries -- that is, to Lie groupoids and their higher versions -- is a problem that has interested many mathematicians in the last decades. In the early 2000's, Crainic and Fernandes proposed in a seminal paper a path-integration of Lie algebroids. This beautiful method has a lot of analytical difficulties. Now that the adjoint representation (up to homotopy) of a Lie algebroid is well-understood, we propose to study the integration problem from a new and more algebraic point of view, extending van Est's method for integrating Lie algebras.

李代数体及其更高形式的李代数体是微分分次流形，它们刻画了无穷小的对称。将这些结构集成到编码全局对称性的结构--即李群胚及其更高版本--是过去几十年来许多数学家感兴趣的问题。2000年初，S、克雷尼克和费尔南德斯在一篇开创性的论文中提出了李代数体的路径积分。这种漂亮的方法有很多分析上的困难。既然李代数体的伴随表示(直到同伦)已经被很好地理解，我们建议从一个新的更代数的角度来研究积分问题，推广van Est的李代数积分方法。