李代数、李群?
前面介绍说代数几何串联了绝大多数数学分支,但其实那里的看法并不准确,最近又了解到,精通微分几何的数学家可能对代数几何一窍不通也是有可能的,原因是数学分支之间的分歧实在太大。
Lie Theory更像是潜藏在各个角落的数学,真正成就Lie Theory在现代数学中的地位的人是Elie Cartan。
While Lie had many fertile ideas, Cartan was primarily responsible for the extensions and applications of his theory that have made it a basic component of modern mathematics. It was he who, with some help from Weyl, developed the seminal, essentially algebraic ideas of Killing into the theory of the structure and representation of semisimple Lie algebras that plays such a fundamental role in present-day Lie theory. And although Lie envisioned applications of his theory to geometry, it was Cartan who actually created them, for example through his theories of symmetric and generalized spaces, including all the attendant apparatus (moving frames, exterior differential forms, etc.)