This chapter treats Lie groups and their Lie algebras through invariant vector fields, exponential maps and subgroups, before studying smooth group actions, isometries and applications to symmetric space-times.
Contents
- 19.1 Lie groups
- 19.2 The exponential map
- 19.3 Lie subgroups
- 19.4 Lie groups of transformations
- 19.5 Groups of isometries
Concept index
Terms by section. Links lead to the brown underlined definitions in the Chinese reading text.
19.1 Lie groups
- Lie group李群
- left translation左平移
- right translation右平移
- left-invariant vector field左不变向量场
- Lie algebra of a Lie group李群的李代数
- structure constants结构常数
- left-invariant differential form左不变微分形式
- Maurer–Cartan relations毛雷尔–卡当关系
19.2 The exponential map
19.3 Lie subgroups
19.4 Lie groups of transformations
- Lie group of transformations李变换群
- effective action有效作用
- orbit轨道
- transitive action传递作用
- homogeneous manifold齐性流形
- isotropy group各向同性群
- adjoint representation伴随表示
- derivation导子