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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.

Mathematical records
Object	Kind	Essential data	Coverage
$\mathfrak{sl}(2, \mathbb C)$ sl(2, C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 3	reference Sourced record
$\mathfrak{sl}(3, \mathbb C)$ sl(3, C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 8	reference Sourced record
$\mathfrak{sl}(4, \mathbb C)$ sl(4, C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 15	reference Sourced record
$\mathfrak{sl}(5, \mathbb C)$ sl(5, C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 24	reference Sourced record
$\mathfrak{so}(5, \mathbb C) \cong \mathfrak{sp}(4, \mathbb C)$ so(5, C) ≅ sp(4, C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 10	reference Sourced record
$\mathfrak{sp}(6, \mathbb C)$ sp(6, C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 21	reference Sourced record
$\mathfrak{so}(8, \mathbb C)$ so(8, C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 28	reference Sourced record
$\mathfrak{so}(10, \mathbb C)$ so(10, C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 45	reference Sourced record
$\mathfrak{e}_{6}(\mathbb C)$ e₆(C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 78	reference Sourced record
$\mathfrak{e}_{7}(\mathbb C)$ e₇(C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 133	reference Sourced record
$\mathfrak{e}_{8}(\mathbb C)$ e₈(C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 248	reference Sourced record
$\mathfrak{f}_{4}(\mathbb C)$ f₄(C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 52	reference Sourced record
$\mathfrak{g}_{2}(\mathbb C)$ g₂(C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 14	reference Sourced record
$\mathfrak{sl}(2, \mathbb C) \oplus \mathfrak{sl}(2, \mathbb C)$ sl(2, C) ⊕ sl(2, C) — complex Lie algebra	Lie algebra Lie theory	dimℂ 6	reference Sourced record
$(\mathbb C,[\, ,\,]=0)$ C (zero bracket) — complex Lie algebra	Lie algebra Lie theory	dimℂ 1	reference Sourced record
$\mathfrak{sl}(2, \mathbb C) \oplus \mathbb C$ sl(2, C) ⊕ C — complex Lie algebra	Lie algebra Lie theory	dimℂ 4	reference Sourced record
$\mathfrak{su}(2)$ su(2) — real Lie algebra	Lie algebra Lie theory	dimℝ 3	reference Sourced record
$\mathfrak{su}(3)$ su(3) — real Lie algebra	Lie algebra Lie theory	dimℝ 8	reference Sourced record
$\mathfrak{su}(4) \cong \mathfrak{so}(6)$ su(4) ≅ so(6) — real Lie algebra	Lie algebra Lie theory	dimℝ 15	reference Sourced record
$\mathfrak{su}(5)$ su(5) — real Lie algebra	Lie algebra Lie theory	dimℝ 24	reference Sourced record
$\mathfrak{sp}(2) \cong \mathfrak{so}(5)$ sp(2) ≅ so(5) — real Lie algebra	Lie algebra Lie theory	dimℝ 10	reference Sourced record
$\mathfrak{sp}(3)$ sp(3) — real Lie algebra	Lie algebra Lie theory	dimℝ 21	reference Sourced record
$\mathfrak{so}(8)$ so(8) — real Lie algebra	Lie algebra Lie theory	dimℝ 28	reference Sourced record
$\mathfrak{so}(10)$ so(10) — real Lie algebra	Lie algebra Lie theory	dimℝ 45	reference Sourced record
$\mathfrak{e}_{6}\;\text{compact}$ e₆ compact — real Lie algebra	Lie algebra Lie theory	dimℝ 78	reference Sourced record
$\mathfrak{e}_{7}\;\text{compact}$ e₇ compact — real Lie algebra	Lie algebra Lie theory	dimℝ 133	reference Sourced record
$\mathfrak{e}_{8}\;\text{compact}$ e₈ compact — real Lie algebra	Lie algebra Lie theory	dimℝ 248	reference Sourced record
$\mathfrak{f}_{4}\;\text{compact}$ f₄ compact — real Lie algebra	Lie algebra Lie theory	dimℝ 52	reference Sourced record
$\mathfrak{g}_{2}\;\text{compact}$ g₂ compact — real Lie algebra	Lie algebra Lie theory	dimℝ 14	reference Sourced record
$\mathfrak{su}(2) \oplus \mathfrak{su}(2)$ su(2) ⊕ su(2) — real Lie algebra	Lie algebra Lie theory	dimℝ 6	reference Sourced record
$\mathfrak{u}(1)$ u(1) — real Lie algebra	Lie algebra Lie theory	dimℝ 1	reference Sourced record
$\mathfrak{u}(2)$ u(2) — real Lie algebra	Lie algebra Lie theory	dimℝ 4	reference Sourced record
$\mathfrak{sl}(2, \mathbb R)$ sl(2, R) — real Lie algebra	Lie algebra Lie theory	dimℝ 3	reference Sourced record
$\mathfrak{sl}(3, \mathbb R)$ sl(3, R) — real Lie algebra	Lie algebra Lie theory	dimℝ 8	reference Sourced record
$\mathfrak{su}(2,2) \cong \mathfrak{so}(2,4)$ su(2,2) ≅ so(2,4) — real Lie algebra	Lie algebra Lie theory	dimℝ 15	reference Sourced record
$\mathfrak{sp}(4, \mathbb R) \cong \mathfrak{so}(2,3)$ sp(4, R) ≅ so(2,3) — real Lie algebra	Lie algebra Lie theory	dimℝ 10	reference Sourced record
$\mathfrak{sl}(2,\mathbb C)_{\mathbb R}$ sl(2, C) viewed over R — real Lie algebra	Lie algebra Lie theory	dimℝ 6	reference Sourced record
$\mathfrak{su}(3)\oplus\mathfrak{su}(2)\oplus\mathfrak u(1)$ Compact Standard Model gauge algebra	Lie algebra Lie theory	dimℝ 12	reference Sourced record

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Finite-simple classification Lie classification