Curated collection
Gauge groups and global forms
Compact groups, central quotients, and covering maps relevant to gauge theory. Group data constrain a theory; matter and line-operator choices belong to a physical setup.
31 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 |
| U(1) Circle group | Group Lie theory | dimℝ 1 | reference Sourced record |
| Spin(4) Euclidean spin group in four dimensions | Group Lie theory | dimℝ 6 | reference 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 |
| U(2) Unitary group in two dimensions | Group Lie theory | dimℝ 4 | reference Sourced record |
| SO(4) Rotation group in four dimensions | Group Lie theory | dimℝ 6 | reference Sourced record |
| 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 |
| SU(3) × SU(2) × U(1) Standard Model compact covering product | Group Lie theory | dimℝ 12 | executable 3 linked workbenchs |
| G_SM^(2) Standard Model global group with diagonal Z2 quotient | Group Lie theory | dimℝ 12 | executable 3 linked workbenchs |
| G_SM^(3) Standard Model global group with diagonal Z3 quotient | Group Lie theory | dimℝ 12 | executable 3 linked workbenchs |
| G_SM^(6) Standard Model global group with diagonal Z6 quotient | Group Lie theory | dimℝ 12 | executable 3 linked workbenchs |