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49finite group records41Lie group records38Lie algebras22specified maps

22 released records. Individual groups and parameterized families are counted separately.

Mathematical records
Object	Kind	Essential data	Coverage
$\mathrm{SU}(2) \longrightarrow \mathrm{SO}(3)$ Spin cover of three-dimensional rotations	Map Lie theory	SO(3)	executable 1 linked workbench
$\mathrm{SU}(3) \longrightarrow \mathrm{PSU}(3)$ Adjoint quotient of SU(3)	Map Lie theory	PSU(3)	executable 1 linked workbench
$\mathrm{SU}(2) \hookrightarrow \mathrm{SU}(3)$ Regular block inclusion in SU(3)	Map Lie theory	{diag(A,1) : A ∈ SU(2)} ≅ SU(2)	executable 2 linked workbenchs
$\mathrm{SU}(2) \longrightarrow \mathrm{SU}(3),\quad j=1$ Principal spin-one homomorphism into SU(3)	Map Lie theory	An SU(3)-conjugate of the real SO(3) subgroup	executable 2 linked workbenchs
$\mathrm{U}(1) \hookrightarrow \mathrm{SU}(2)$ Normalized maximal torus of SU(2)	Map Lie theory	{diag(z,z⁻¹) : \|z\|=1}	executable 1 linked workbench
$\mathrm{U}(1) \cong \mathrm{SO}(2) \hookrightarrow \mathrm{SO}(3)$ Normalized axial rotation subgroup of SO(3)	Map Lie theory	Rotations fixing a chosen oriented axis, isomorphic to SO(2)	executable 1 linked workbench
$\mathrm{Spin}(4) \longrightarrow \mathrm{SO}(4)$ Quaternionic spin cover in four Euclidean dimensions	Map Lie theory	SO(4)	reference Sourced record
$\mathrm{SU}(4) \longrightarrow \mathrm{SO}(6)$ Exterior-square realization of the Spin(6) cover	Map Lie theory	SO(6)	reference Sourced record
$\mathrm{SU}(4) \longrightarrow \mathrm{PSU}(4)$ Full central quotient of SU(4)	Map Lie theory	PSU(4)	reference Sourced record
$\mathrm{Sp}(2) \longrightarrow \mathrm{SO}(5)$ Quaternionic construction of the Spin(5) cover	Map Lie theory	SO(5)	reference Sourced record
$\mathrm{Spin}(8) \longrightarrow \mathrm{SO}(8)$ Vector spin cover in eight Euclidean dimensions	Map Lie theory	SO(8)	reference Sourced record
$\mathrm{Spin}(10) \longrightarrow \mathrm{SO}(10)$ Vector spin cover in ten Euclidean dimensions	Map Lie theory	SO(10)	reference Sourced record
$\mathrm{SL}(2, \mathbb C) \longrightarrow \mathrm{SO}_0(1,3)$ Hermitian-matrix Lorentz spin cover	Map Lie theory	SO₀(1,3)	reference Sourced record
$\mathrm{SL}(2, \mathbb R) \longrightarrow \mathrm{PSL}(2, \mathbb R)$ Adjoint central quotient of SL(2,R)	Map Lie theory	PSL(2,R) ≅ SO₀(2,1)	reference Sourced record
$\widetilde{\mathrm{SL}(2,\mathbb R)} \longrightarrow \mathrm{SL}(2,\mathbb R)$ Universal covering map of SL(2,R)	Map Lie theory	SL(2,R)	reference Sourced record
$\mathrm{SU}(2,2) \longrightarrow \mathrm{SO}_0(2,4)$ Exterior-square spin cover in signature (2,4)	Map Lie theory	SO₀(2,4)	reference Sourced record
$\mathrm{Sp}(4, \mathbb R) \longrightarrow \mathrm{SO}_0(2,3)$ Primitive-exterior-square spin cover in signature (2,3)	Map Lie theory	SO₀(2,3)	reference Sourced record
$G_{\mathrm{SM}}^{(1)}\longrightarrow G_{\mathrm{SM}}^{(2)}$ Standard Model quotient map of order 2	Map Lie theory	G_SM^(2)	executable 1 linked workbench
$G_{\mathrm{SM}}^{(1)}\longrightarrow G_{\mathrm{SM}}^{(3)}$ Standard Model quotient map of order 3	Map Lie theory	G_SM^(3)	executable 1 linked workbench
$G_{\mathrm{SM}}^{(1)}\longrightarrow G_{\mathrm{SM}}^{(6)}$ Standard Model quotient map of order 6	Map Lie theory	G_SM^(6)	executable 1 linked workbench
$SU(3)\times SU(2)\times U(1)_X\longrightarrow SU(5)$ Color-first SU(5) block homomorphism	Map Lie theory	S(U(3) × U(2))	executable 1 linked workbench
$G_{\mathrm{SM}}^{(6)}\hookrightarrow SU(5)$ 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.

Finite-simple classification Lie classification