In this chapter we allow for yet another law of composition to be imposed on vector spaces, whereby the product of any two vectors results in another vector from the same vector space. Structures of this kind are generically called algebras and arise naturally in a variety of contexts [1, 2].
Contents
- 6.1 Algebras and ideals
- 6.2 Complex numbers and complex structures
- 6.3 Quaternions and Clifford algebras
- 6.4 Grassmann algebras
- 6.5 Lie algebras and Lie groups
Concept index
Terms by section. Links lead to the brown underlined definitions in the Chinese reading text.
6.1 Algebras and ideals
- algebra代数
- associative algebra结合代数
- commutative algebra交换代数
- structure constants结构常数
- algebra homomorphism代数同态
- subalgebra子代数
- algebra isomorphism代数同构
- left ideal左理想
- right ideal右理想
- two-sided ideal双边理想
- ideal理想
6.2 Complex numbers and complex structures
6.3 Quaternions and Clifford algebras
- quaternion四元数
- scalar part标量部
- vector part向量部
- conjugate quaternion共轭四元数
- pure quaternion纯四元数
- Clifford algebra克利福德代数
- spinor旋量
6.4 Grassmann algebras
- simple 2-vector简单二向量
- bivector二重向量
- multivector多重向量
- exterior product外积
- Grassmann algebra格拉斯曼代数
- exterior algebra外代数
- graded algebra分次代数