Construction of miniversal deformations of Lie algebras

被引:76
作者
Fialowski, A
Fuchs, D
机构
[1] Eotvos Lorand Univ, Dept Appl Anal, H-1088 Budapest, Hungary
[2] Univ Calif Davis, Dept Math, Davis, CA 95616 USA
关键词
D O I
10.1006/jfan.1998.3349
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider deformations of finite or infinite dimensional Lie algebras over a held of characteristic 0. There is substantial confusion in the literature if one tries to describe all the non-equivalent deformations of a given Lie algebra. It is known that there is in general no "universal" deformation of a Lie algebra L with a commutative algebra base A with the properly that for any other deformation of L with base B there exists a unique homomorphism f: A --> B that induces an equivalent deformation. Thus one is led to seek a miniversal deformation. For a miniversal deformation such a homomorphism exists, but is unique only at the first level. If we consider deformations with base spec A, where A is a local algebra, then under some minor restrictions there exists a miniversal element. In this paper we give a construction of a miniversal deformation. (C) 1999 Academic Press.
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页码:76 / 110
页数:35
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