lecture-notes
Haber · Spin covers and subgroup examples
Howard E. Haber
Use in this reference: Linked source with original summaries of mathematical facts. Consult the source for its own terms; no blanket redistribution license is asserted.
Relevant material: Spring 2017; Spin(4) on pages 7–8, SU(2) and SO(3) subgroups of SU(3) on pages 14–15.
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| SU(2) | Explicit homomorphism | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) | Explicit homomorphism | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(3) | Explicit homomorphism | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(3) | Explicit homomorphism | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| Spin(4) | Representations | Pages 7–8: SU(2) × SU(2) and the diagonal order-two SO(4) kernel |
| Spin(4) | In physics | Applications to the indicated symmetry and representation category |
| Spin(4) | Explicit homomorphism | Pages 7–8: SU(2) × SU(2) and SO(4) |
| SO(4) | Representation category and descent | Pages 7–8: SU(2) × SU(2) and SO(4) |
| SU(2) ↪ SU(3) | Definition | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Domain | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Codomain | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Specified homomorphism | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Kernel | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Image | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Injective | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Surjective | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Global and representation consequences | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Global and representation consequences | Problem 5: regular inclusion |
| SU(2) ↪ SU(3) | Domain group | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) ↪ SU(3) | Codomain group | Problem 5, pages 14–15: block SU(2) subgroup of SU(3) |
| SU(2) → SU(3), spin 1 | Definition | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Domain | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Codomain | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Specified homomorphism | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Kernel | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Image | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Injective | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Surjective | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Global and representation consequences | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Domain group | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| SU(2) → SU(3), spin 1 | Codomain group | Problem 5, pages 14–15: the irreducible three-dimensional SU(2) action and SO(3) image |
| Spin(4) → SO(4) | Definition | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Domain | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Codomain | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Specified homomorphism | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Kernel | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Image | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Injective | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Surjective | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Covering degree | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Global and representation consequences | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Domain group | Pages 7–8: SU(2) × SU(2) and SO(4) |
| Spin(4) → SO(4) | Codomain group | Pages 7–8: SU(2) × SU(2) and SO(4) |