maximalTorus
P78391
predicate
Indicates that one group is a maximal torus inside another group, meaning it is a largest possible connected, abelian, diagonalizable subgroup not properly contained in any larger such torus.
Observed surface forms (2)
- hasMaximalTorus ×3
- isMaximalTorusIn ×2
Sample triples (7)
| Subject | Object |
|---|---|
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
diagonal invertible matrices via predicate surface "hasMaximalTorus" ⓘ |
|
special linear group SL(n,C)
surface form:
SL(n,ℂ)
|
diagonal matrices with determinant 1 via predicate surface "hasMaximalTorus" ⓘ |
|
rotation group SO(3)
surface form:
SO(3)
|
special orthogonal group SO(n)
ⓘ
surface form:
SO(2)
|
|
rotation group SU(2)
surface form:
SU(2)
|
U(1) via predicate surface "hasMaximalTorus" ⓘ |
|
special unitary group SU(n)
surface form:
SU(n)
|
diagonal unitary matrices with determinant 1 ⓘ |
| U(1) | SU(2) via predicate surface "isMaximalTorusIn" ⓘ |
| U(1) | U(n) via predicate surface "isMaximalTorusIn" ⓘ |