凹凸函數與李群

Abstract

令V為一n 維的向量空間，且附有一個非退化的對稱雙線形式。令G為V上保持此雙線形式的線性函數所組成的群。此論文探討G及其軌道的拓樸性質，以及G的李代數。

Let V be an n-dimensional vector space, equipped with a non-degenerate symmetic bilinear form. Let G be the group of all linear mappings on V which preserves this bilinear form. In this thesis, we study the topological properties of G and its orbits, as well as the Lie algebra of G.