Deformations of homomorphisms of Lie groups and Lie algebras
Deformations of homomorphisms of Lie groups and Lie algebras
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李群和李代数同态的变形
DOI：
10.1090/s0002-9904-1967-11703-8
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发表时间：
1967
影响因子：
1.3
通讯作者：
R. Richardson
中科院分区：
文献类型：
--
作者：
A. Nijenhuis;R. Richardson
本文的目的是公布李群和李代数的同态变形的几个结果。我们的主要定理是紧流形上复解析结构变形的两个基本定理的精确类似物，即Frölicher-Nijenhuis [3]的刚性定理和Kuranishi fs]的局部完备性定理。在我们的结果中，层上同调被李群和李代数的上同调所取代。我们的证明在很大程度上依赖于[9]中发展的分次李代数（GLA）的变形理论。我们的结果李代数同态立即从那里给出的结果，一旦适当的GLA的定义。李群同态结果的详细证明（仅在此概述）将在其他地方出现。
The purpose of this note is to announce several results on deformations of homomorphisms of Lie groups and Lie algebras. Our main theorems are precise analogues of two basic theorems on deformations of complex analytic structures on compact manifolds, the rigidity theorem of Frölicher-Nijenhuis [3] and the local completeness theorem of Kuranishi fs]. In our results, sheaf cohomology is replaced by the cohomology of Lie groups and Lie algebras. Our proofs rely heavily on the theory of deformations in graded Lie algebras (GLA's) developed in [9]. Our results on Lie algebra homomorphisms follow immediately from the results given there, once the appropriate GLA is defined. Detailed proofs of the results on Lie group homomorphisms (which are only outlined here) will appear elsewhere.