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Lie algebra records.
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49finite group records41Lie group records38Lie algebras22specified maps
38 released records. Individual groups and parameterized families are counted separately.
| Object | Kind | Essential data | Coverage |
|---|---|---|---|
| sl(2, C) sl(2, C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 3 | reference Sourced record |
| sl(3, C) sl(3, C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 8 | reference Sourced record |
| sl(4, C) sl(4, C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 15 | reference Sourced record |
| sl(5, C) sl(5, C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 24 | reference Sourced record |
| so(5, C) ≅ sp(4, C) so(5, C) ≅ sp(4, C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 10 | reference Sourced record |
| sp(6, C) sp(6, C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 21 | reference Sourced record |
| so(8, C) so(8, C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 28 | reference Sourced record |
| so(10, C) so(10, C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 45 | reference Sourced record |
| e₆(C) e₆(C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 78 | reference Sourced record |
| e₇(C) e₇(C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 133 | reference Sourced record |
| e₈(C) e₈(C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 248 | reference Sourced record |
| f₄(C) f₄(C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 52 | reference Sourced record |
| g₂(C) g₂(C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 14 | reference Sourced record |
| sl(2, C) ⊕ sl(2, C) sl(2, C) ⊕ sl(2, C) — complex Lie algebra | Lie algebra Lie theory | dimℂ 6 | reference Sourced record |
| C (zero bracket) C (zero bracket) — complex Lie algebra | Lie algebra Lie theory | dimℂ 1 | reference Sourced record |
| sl(2, C) ⊕ C sl(2, C) ⊕ C — complex Lie algebra | Lie algebra Lie theory | dimℂ 4 | reference Sourced record |
| su(2) su(2) — real Lie algebra | Lie algebra Lie theory | dimℝ 3 | reference Sourced record |
| su(3) su(3) — real Lie algebra | Lie algebra Lie theory | dimℝ 8 | reference Sourced record |
| su(4) ≅ so(6) su(4) ≅ so(6) — real Lie algebra | Lie algebra Lie theory | dimℝ 15 | reference Sourced record |
| su(5) su(5) — real Lie algebra | Lie algebra Lie theory | dimℝ 24 | reference Sourced record |
| sp(2) ≅ so(5) sp(2) ≅ so(5) — real Lie algebra | Lie algebra Lie theory | dimℝ 10 | reference Sourced record |
| sp(3) sp(3) — real Lie algebra | Lie algebra Lie theory | dimℝ 21 | reference Sourced record |
| so(8) so(8) — real Lie algebra | Lie algebra Lie theory | dimℝ 28 | reference Sourced record |
| so(10) so(10) — real Lie algebra | Lie algebra Lie theory | dimℝ 45 | reference Sourced record |
| e₆ compact e₆ compact — real Lie algebra | Lie algebra Lie theory | dimℝ 78 | reference Sourced record |
| e₇ compact e₇ compact — real Lie algebra | Lie algebra Lie theory | dimℝ 133 | reference Sourced record |
| e₈ compact e₈ compact — real Lie algebra | Lie algebra Lie theory | dimℝ 248 | reference Sourced record |
| f₄ compact f₄ compact — real Lie algebra | Lie algebra Lie theory | dimℝ 52 | reference Sourced record |
| g₂ compact g₂ compact — real Lie algebra | Lie algebra Lie theory | dimℝ 14 | reference Sourced record |
| su(2) ⊕ su(2) su(2) ⊕ su(2) — real Lie algebra | Lie algebra Lie theory | dimℝ 6 | reference Sourced record |
| u(1) u(1) — real Lie algebra | Lie algebra Lie theory | dimℝ 1 | reference Sourced record |
| u(2) u(2) — real Lie algebra | Lie algebra Lie theory | dimℝ 4 | reference Sourced record |
| sl(2, R) sl(2, R) — real Lie algebra | Lie algebra Lie theory | dimℝ 3 | reference Sourced record |
| sl(3, R) sl(3, R) — real Lie algebra | Lie algebra Lie theory | dimℝ 8 | reference Sourced record |
| su(2,2) ≅ so(2,4) su(2,2) ≅ so(2,4) — real Lie algebra | Lie algebra Lie theory | dimℝ 15 | reference Sourced record |
| sp(4, R) ≅ so(2,3) sp(4, R) ≅ so(2,3) — real Lie algebra | Lie algebra Lie theory | dimℝ 10 | reference Sourced record |
| sl(2, C) viewed over R sl(2, C) viewed over R — real Lie algebra | Lie algebra Lie theory | dimℝ 6 | reference Sourced record |
| su(3) ⊕ su(2) ⊕ u(1) Compact Standard Model gauge algebra | Lie algebra Lie theory | dimℝ 12 | 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.