On generalized graded Lie algebras and geometric structures I
On generalized graded Lie algebras and geometric structures I
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论广义分级李代数和几何结构 I
DOI：
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发表时间：
1967
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通讯作者：
N. Tanaka
中科院分区：
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作者：
N. Tanaka
本文的主要目的是为某些无限类型甚至非椭圆的线性群结构建立一个新的延展定理，并将该定理应用于微分系统的几何（Chevalley意义上的分布）和复流形中实子流形的几何。 （如果 $G$ 的李代数 $mathfrak{g}$ 不包含 1 阶矩阵，则线性群 $G$ 称为椭圆形；如果线性群 $G$ 是椭圆形，则 G 结构称为椭圆形。Ochiai [4] 最近的工作表明，当且仅当 G 结构的无穷小自同构的定义方程形成线性微分的椭圆系统时，G 结构才是椭圆形的方程）。首先，我们介绍广义分级李代数的概念（定义2.1）。设 $mathfrak{g}$ 为李代数，并设 $(mathfrak{g}_{p})_{pin Z}$ 为以下子空间族
The main purpose of the present paper is to establish a new prolongation theorem for certain linear group structures which are of infinite type and even not elliptic, and is to apply this theorem to the geometry of differential systems (distributions in the sense of Chevalley) and the geometry of real submanifolds in complex manifolds. (A linear group $G$ is called elliptic if the Lie algebra $mathfrak{g}$ of $G$ contains no matrix of rank 1, and a G-structure is called elliptic if the linear group $G$ is elliptic. A recent work of Ochiai [4] has shown that a G-structure is elliptic if and only if the defining equation of infinitesimal automorphisms of the G-structure forms an elliptic system of linear differential equations). First of all, we introduce the notion of a generalized graded Lie algebra (Def. 2.1). Let $mathfrak{g}$ be a Lie algebra, and let $(mathfrak{g}_{p})_{pin Z}$ be a family of subspaces of