Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group orthogonal group compact group |
| gptkbp:actsOn |
complex projective space CP^n
|
| gptkbp:centralTo |
cyclic group of order n+1
|
| gptkbp:connects |
true
|
| gptkbp:definedIn |
group of (n+1)×(n+1) unitary matrices with determinant 1
|
| gptkbp:dimensions |
n^2+2n
|
| gptkbp:example |
SU(2) is isomorphic to the group of unit quaternions
SU(3) is used in quantum chromodynamics |
| gptkbp:field |
complex numbers
|
| gptkbp:fundamentalGroup |
Z_{n+1}
|
| gptkbp:hasSubgroup |
U(n+1)
|
| https://www.w3.org/2000/01/rdf-schema#label |
SU(n+1) Lie group
|
| gptkbp:isQuotientOf |
PSU(n+1)
|
| gptkbp:Lie_algebra |
su(n+1)
|
| gptkbp:maximalTorus |
U(1)^n
|
| gptkbp:notation |
SU(n+1)
|
| gptkbp:rank |
n
|
| gptkbp:realForm |
SL(n+1,C)
SL(n+1,R) |
| gptkbp:simplyConnected |
true
|
| gptkbp:type |
A_n
|
| gptkbp:usedIn |
gptkb:gauge_theory
gptkb:theoretical_physics differential geometry particle physics quantum mechanics representation theory |
| gptkbp:bfsParent |
gptkb:A_n_root_lattice
|
| gptkbp:bfsLayer |
6
|