形变理论综述(二):同伦方法（英文）

发布时间：2023-05-21 21:56

　　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.

【文章页数】：21 页

【文章目录】：
0 Introduction
1 Closed Model Categories
2 Brown Representability Theorem for Compactly Gener-ated Model Categories
3 MC Elements and MC Moduli Sets
    3.1 MC Moduli in dg Lie Algebras
    3.2 MC Moduli in dg Algebras
4 Koszul Duality
    4.1 dg Coalgebras and Pseudocompact dg Algebras
    4.2 Quillen Equivalence between DGLA and
    4.3 Quillen Equivalence between DGA/k and
    4.4 Relationship between Two Types of Koszul Duality
5 Main Theorems
    5.1 MC Elements and the Deformation Functor based on a dg Lie Algebra
    5.2 Finding a dg Lie Algebra associated with a Deformation Functor
    5.3 Associative Deformation Theory
    5.4 Finding a dg Algebra Associated with a Deformation Functor
    5.5 Comparing Commutative and Associative Deformations



本文编号：3821497