广义对称空间及其性质

Generalized Symmetric Spaces and some of Their Properties

G/H表示由李群G的一个对合自同构所决定的齐性对称空间。本文把李群的单个对合自同构推广为由李群 G 的一些自同构组成的有限可换群,从而决定了一个广义对称空间,并讨论了它的某些性质。

Let G / H be a homogeneous symmetric space, where H is the fixed point set of an involutive automorphism of Lie group G. Generalizing a single involutive automorphism to a finite Abelian group of automorphisms of G, we obtain a homogeneous space called generalized symmetric space and some of its properties.