Curated collection
Compact groups with simple Lie algebra
Choose the Lie type and then the global form. A simply connected cover and a central quotient are distinct global group records.
32 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 |
| SO(3) Rotation group in three dimensions | Group Lie theory | dimℝ 3 | executable 2 linked workbenchs |
| SU(3) Special unitary group | Group Lie theory | dimℝ 8 | executable 8 linked workbenchs |
| PSU(3) Projective special unitary group | Group Lie theory | dimℝ 8 | executable 1 linked workbench |
| Aᵣ Simple Lie type Aᵣ | Family Lie theory | Parameterized family | classification Sourced record |
| Bᵣ Simple Lie type Bᵣ | Family Lie theory | Parameterized family | classification Sourced record |
| Cᵣ Simple Lie type Cᵣ | Family Lie theory | Parameterized family | classification Sourced record |
| Dᵣ Simple Lie type Dᵣ | Family Lie theory | Parameterized family | classification Sourced record |
| E₆ Simple Lie type E₆ | Family Lie theory | Parameterized family | classification Sourced record |
| E₇ Simple Lie type E₇ | Family Lie theory | Parameterized family | classification Sourced record |
| E₈ Simple Lie type E₈ | Family Lie theory | Parameterized family | classification Sourced record |
| F₄ Simple Lie type F₄ | Family Lie theory | Parameterized family | classification Sourced record |
| G₂ Simple Lie type G₂ | Family Lie theory | Parameterized family | classification Sourced record |
| SU(4) Special unitary group in four dimensions | Group Lie theory | dimℝ 15 | executable 4 linked workbenchs |
| PSU(4) Adjoint compact group of type A₃ | Group Lie theory | dimℝ 15 | reference Sourced record |
| SU(5) Special unitary group in five dimensions | Group Lie theory | dimℝ 24 | executable 4 linked workbenchs |
| SO(5) Rotation group in five dimensions | Group Lie theory | dimℝ 10 | reference Sourced record |
| SO(6) Rotation group in six dimensions | Group Lie theory | dimℝ 15 | reference Sourced record |
| Sp(2) Compact symplectic group of quaternionic rank two | Group Lie theory | dimℝ 10 | executable 1 linked workbench |
| Sp(3) Compact symplectic group of quaternionic rank three | Group Lie theory | dimℝ 21 | reference Sourced record |
| Spin(8) Simply connected compact spin group in eight dimensions | Group Lie theory | dimℝ 28 | executable 1 linked workbench |
| SO(8) Rotation group in eight dimensions | Group Lie theory | dimℝ 28 | reference Sourced record |
| PSO(8) Adjoint compact group of type D₄ | Group Lie theory | dimℝ 28 | reference Sourced record |
| Spin(10) Simply connected compact spin group in ten dimensions | Group Lie theory | dimℝ 45 | executable 1 linked workbench |
| SO(10) Rotation group in ten dimensions | Group Lie theory | dimℝ 45 | reference Sourced record |
| G₂ compact Compact group of octonion automorphisms | Group Lie theory | dimℝ 14 | executable 1 linked workbench |
| F₄ compact Compact exceptional group of type F₄ | Group Lie theory | dimℝ 52 | executable 1 linked workbench |
| E₆ compact, simply connected Simply connected compact exceptional group of type E₆ | Group Lie theory | dimℝ 78 | executable 1 linked workbench |
| E₇ compact, simply connected Simply connected compact exceptional group of type E₇ | Group Lie theory | dimℝ 133 | executable 1 linked workbench |
| E₈ compact Compact exceptional group of type E₈ | Group Lie theory | dimℝ 248 | executable 1 linked workbench |
| E₆ compact, adjoint Adjoint compact exceptional group of type E₆ | Group Lie theory | dimℝ 78 | reference Sourced record |
| E₇ compact, adjoint Adjoint compact exceptional group of type E₇ | Group Lie theory | dimℝ 133 | reference Sourced record |