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49finite group records41Lie group records38Lie algebras22specified maps
22 released records. Individual groups and parameterized families are counted separately.
| Object | Kind | Essential data | Coverage |
|---|---|---|---|
| SU(2) → SO(3) Spin cover of three-dimensional rotations | Map Lie theory | SO(3) | executable 1 linked workbench |
| SU(3) → PSU(3) Adjoint quotient of SU(3) | Map Lie theory | PSU(3) | executable 1 linked workbench |
| SU(2) ↪ SU(3) Regular block inclusion in SU(3) | Map Lie theory | {diag(A,1) : A ∈ SU(2)} ≅ SU(2) | executable 2 linked workbenchs |
| 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 |
| U(1) ↪ SU(2) Normalized maximal torus of SU(2) | Map Lie theory | {diag(z,z⁻¹) : |z|=1} | executable 1 linked workbench |
| U(1) ≅ SO(2) ↪ SO(3) Normalized axial rotation subgroup of SO(3) | Map Lie theory | Rotations fixing a chosen oriented axis, isomorphic to SO(2) | executable 1 linked workbench |
| 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 |
| SU(4) → PSU(4) Full central quotient of SU(4) | Map Lie theory | PSU(4) | 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 |
| SL(2, R) → PSL(2, R) Adjoint central quotient of SL(2,R) | Map Lie theory | PSL(2,R) ≅ SO₀(2,1) | reference Sourced record |
| Universal SL(2,R) cover → SL(2,R) Universal covering map of SL(2,R) | Map Lie theory | SL(2,R) | 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 |
| G_SM^(1) → G_SM^(2) Standard Model quotient map of order 2 | Map Lie theory | G_SM^(2) | executable 1 linked workbench |
| G_SM^(1) → G_SM^(3) Standard Model quotient map of order 3 | Map Lie theory | G_SM^(3) | executable 1 linked workbench |
| G_SM^(1) → G_SM^(6) Standard Model quotient map of order 6 | Map Lie theory | G_SM^(6) | executable 1 linked workbench |
| SU(3) × SU(2) × U(1)_X → SU(5) Color-first SU(5) block homomorphism | Map Lie theory | S(U(3) × U(2)) | executable 1 linked workbench |
| G_SM^(6) ↪ SU(5) The diagonal-Z6 Standard Model group inside SU(5) | Map Lie theory | S(U(3) × U(2)) | reference Sourced record |
Coverage is specific. Classification identifies a mathematical object or family. Reference supplies stated properties. Executable links to a bounded calculation. Read the coverage policy.