lecture-notes
Brian Conrad, Fundamental Groups of Lie Groups
Brian Conrad
Use in this reference: Linked primary source; the product-group specialization is derived in the local method page.
Relevant material: pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| su(3) ⊕ su(2) ⊕ u(1) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Real dimension | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Rank | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Lie-algebra center | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Simple | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Global groups and charge normalization | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Color algebra | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Weak algebra | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Abelian algebra | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Compact global form with quotient order 1 | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Compact global form with quotient order 2 | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Compact global form with quotient order 3 | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| su(3) ⊕ su(2) ⊕ u(1) | Compact global form with quotient order 6 | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Real dimension | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Rank | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Compact | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Connected | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Fundamental group | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Specified quotient order | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Abstract center | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Matter and the embedded kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Matter and the embedded kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Topology and the universal cover | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Hypercharge and SU(5) | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | The common gauge algebra | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Diagonal quotient of order 2 | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Diagonal quotient of order 3 | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1) | Diagonal quotient of order 6 | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Real dimension | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Rank | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Compact | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Connected | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Fundamental group | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Specified quotient order | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Abstract center | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Matter and the embedded kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Matter and the embedded kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Topology and the universal cover | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Hypercharge and SU(5) | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | The common gauge algebra | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(2) | Specified compact covering product | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Real dimension | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Rank | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Compact | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Connected | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Fundamental group | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Specified quotient order | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Abstract center | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Matter and the embedded kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Matter and the embedded kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Topology and the universal cover | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Hypercharge and SU(5) | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | The common gauge algebra | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(3) | Specified compact covering product | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Real dimension | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Rank | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Compact | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Connected | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Fundamental group | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Specified quotient order | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Abstract center | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Matter and the embedded kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Matter and the embedded kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Topology and the universal cover | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Hypercharge and SU(5) | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | The common gauge algebra | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Specified compact covering product | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) | Block subgroup of SU(5) with the specified map | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(2) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(2) | Kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(2) | Injective | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(2) | Surjective | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(2) | Matter descent | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(2) | Compact covering product | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(2) | Chosen global form | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(3) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(3) | Kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(3) | Injective | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(3) | Surjective | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(3) | Matter descent | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(3) | Compact covering product | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(3) | Chosen global form | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(6) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(6) | Kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(6) | Injective | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(6) | Surjective | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(6) | Matter descent | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(6) | Compact covering product | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(1) → G_SM^(6) | Chosen global form | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Image | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Injective | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Surjective onto SU(5) | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Physical hypercharge | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Keep the charge | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | From homomorphism to embedding | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Underlying compact product, with the X coordinate stated here | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Parent group | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| SU(3) × SU(2) × U(1)_X → SU(5) | Image after converting X to Q=−X | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) ↪ SU(5) | Definition | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) ↪ SU(5) | Kernel | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) ↪ SU(5) | Injective | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) ↪ SU(5) | Image | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) ↪ SU(5) | What the embedding establishes | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) ↪ SU(5) | The specified diagonal quotient | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) ↪ SU(5) | Parent compact group | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |
| G_SM^(6) ↪ SU(5) | Computable block map in the X convention | pp. 1–2: the exact sequence for a connected Lie group modulo a discrete central subgroup |