Curated collection
Spacetime groups and spin covers
Keep dimension, signature, connected component, and covering group visible when discussing fields and states.
23 released records · classifications and individual objects are labeled separately.
| Object | Kind | Essential data | Coverage |
|---|---|---|---|
| SU(2) Special unitary group | Group Lie theory | dimℝ 3 | executable 7 linked workbenchs |
| Spin(4) Euclidean spin group in four dimensions | Group Lie theory | dimℝ 6 | reference Sourced record |
| SL(2,ℂ) Lorentz spin group | Group Lie theory | dimℝ 6 | reference Sourced record |
| Spin(8) Simply connected compact spin group in eight dimensions | Group Lie theory | dimℝ 28 | executable 1 linked workbench |
| Spin(10) Simply connected compact spin group in ten dimensions | Group Lie theory | dimℝ 45 | executable 1 linked workbench |
| SO₀(1,3) Proper orthochronous Lorentz group in four dimensions | Group Lie theory | dimℝ 6 | reference Sourced record |
| SU(2) → SO(3) Spin cover of three-dimensional rotations | Map Lie theory | SO(3) | executable 1 linked workbench |
| SU(2) → SU(3), spin 1 Principal spin-one homomorphism into SU(3) | Map Lie theory | An SU(3)-conjugate of the real SO(3) subgroup | executable 2 linked workbenchs |
| Spin(4) → SO(4) Quaternionic spin cover in four Euclidean dimensions | Map Lie theory | SO(4) | reference Sourced record |
| SU(4) → SO(6) Exterior-square realization of the Spin(6) cover | Map Lie theory | SO(6) | reference Sourced record |
| Sp(2) → SO(5) Quaternionic construction of the Spin(5) cover | Map Lie theory | SO(5) | reference Sourced record |
| Spin(8) → SO(8) Vector spin cover in eight Euclidean dimensions | Map Lie theory | SO(8) | reference Sourced record |
| Spin(10) → SO(10) Vector spin cover in ten Euclidean dimensions | Map Lie theory | SO(10) | reference Sourced record |
| SL(2, C) → SO₀(1,3) Hermitian-matrix Lorentz spin cover | Map Lie theory | SO₀(1,3) | reference Sourced record |
| SU(2,2) → SO₀(2,4) Exterior-square spin cover in signature (2,4) | Map Lie theory | SO₀(2,4) | reference Sourced record |
| Sp(4, R) → SO₀(2,3) Primitive-exterior-square spin cover in signature (2,3) | Map Lie theory | SO₀(2,3) | reference Sourced record |
| D4 · (1,0,0,0) Vector of Spin(8) | Representation Lie theory | dimℂ 8 | executable 1 linked workbench |
| D4 · (0,0,1,0) Half-spin representation of Spin(8) | Representation Lie theory | dimℂ 8 | executable 1 linked workbench |
| D4 · (0,0,0,1) Other half-spin representation of Spin(8) | Representation Lie theory | dimℂ 8 | executable 1 linked workbench |
| D5 · (1,0,0,0,0) Vector of Spin(10) | Representation Lie theory | dimℂ 10 | executable 1 linked workbench |
| D5 · (0,0,0,0,1) Chiral spinor of Spin(10) | Representation Lie theory | dimℂ 16 | executable 1 linked workbench |
| D5 · (0,0,0,1,0) Conjugate chiral spinor of Spin(10) | Representation Lie theory | dimℂ 16 | executable 1 linked workbench |
| D5 · (0,1,0,0,0) Adjoint of Spin(10) | Representation Lie theory | dimℂ 45 | executable 1 linked workbench |