形变理论综述(二):同伦方法  

Review of Deformation Theory Ⅱ:A Homotopical Approach

作　　者：管艾 Andrey Lazarev 生云鹤 唐荣[2] GUAN Ai;Andrey Lazarev;SHENG Yunhe;TANG Rong(Department of Mathematics and Statistics,Lancaster University,Lancaster LA14YF,UK;School of Mathematics,Jilin University,Changchun,Jilin,130012,P.R.China)

机构地区：[1]兰开斯特大学数学与统计学系,兰开斯特,LA14YF,英国 [2]吉林大学数学学院,长春吉林130012

出　　处：《数学进展》2020年第3期278-298,共21页Advances in Mathematics（China）

基　　金：This research was partially supported by NSFC(No.11922110)。

摘　　要：本文从Hinich,Manetti和Pridham在同伦代数上的结果出发,给出形变理论的一个通用方法.特别地,我们证明所有特征为0的形变函子被一个同伦意义下特定的分次李代数控制,同时对任意特征的形变函子给出了非交换的类似结果.We give a general treatment of deformation theory from the point of view of homotopical algebra following Hinich,Manetti and Pridham.In particular,we show that any deformation functor in characteristic zero is controlled by a certain differential graded Lie algebra defined up to homotopy,and also formulate a noncommutative analogue of this result valid in any characteristic.

关 键 词：模型范畴 形变 Maurer-Cartan元 结合代数 李代数 

分 类 号：O154[理学—数学]