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Clifford Algebras and the Classical Groups

克利福德代数及典型群

Cambridge University Press Ian R Porteous

ISBN：9780521118026，出版年：1995，中图分类号：O1 被引 545次

1. Linear spaces 2. Real and complex algebras 3. Exact sequences 4. Real quadratic spaces 5. The classification of quadratic spaces 6. Anti-involutions of R(n) 7. Anti-involutions of C(n) 8. Quarternions 9. Quarternionic linear spaces 10. Anti-involutions of H(n) 11. Tensor products of algebras 12. Anti-involutions of 2K(n) 13. The classical groups 14. Quadric Grassmannians 15. Clifford algebras 16. Spin groups 17. Conjugation 18. 2x2 Clifford matrices 19. The Cayley algebra 20. Topological spaces 21. Manifolds 22. Lie groups 23. Conformal groups 24. Triality.

Classification of Clifford algebras Clifford algebra Representation theory Spin representation Quadratic algebra Lie conformal algebra Classical group Clifford analysis Pure mathematics

Clifford Algebras and Spinors

克利福德代数和旋转子

Cambridge University Press Pertti Lounesto

ISBN：9780521005517，出版年：2001，中图分类号：O1 被引 858次

A historical review of spinors is given together with a construction of spinor spaces as minimal left ideals of Clifford algebras. Spinor spaces of euclidean spaces over reals have a natural linear structure over reals, complex numbers or quaternions. Clifford algebras have involutions which induce bilinear forms or scalar products on spinor spaces. The automorphism groups of these scalar products of spinors are determined and also classified.

Clifford algebra Classification of Clifford algebras Spinor WeylâBrauer matrices Spinors in three dimensions Spin representation Clifford analysis Gamma matrices Pure mathematics Classification of Clifford algebras