hasMaximalCompactSubgroupOf
P78099
predicate
Indicates that one mathematical group is the maximal compact subgroup contained within another group.
Observed surface forms (3)
- hasMaximalCompactSubgroup ×9
- isMaximalCompactSubgroupOf ×2
- maximalCompactSubgroup ×2
Sample triples (14)
| Subject | Object |
|---|---|
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
U(n) via predicate surface "maximalCompactSubgroup" NERFINISHED ⓘ |
|
general linear group GL(n,R)
surface form:
GL(n,ℝ)
|
O(n) via predicate surface "hasMaximalCompactSubgroup" ⓘ |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
PSU(2) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
| PSL(2,ℝ) | SO(2) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
| SL(2,C) |
rotation group SU(2)
via predicate surface "hasMaximalCompactSubgroup"
ⓘ
surface form:
SU(2)
|
| SL(2,R) | SO(2) via predicate surface "maximalCompactSubgroup" NERFINISHED ⓘ |
|
special linear group SL(n,R)
surface form:
SL(2,ℝ)
|
SO(2) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
|
special linear group SL(n,R)
surface form:
SL(n,ℝ)
|
SO(n) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
| SO(2,d-1) | SO(2)×SO(d-1) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
|
special orthogonal group SO(n)
surface form:
SO(n)
|
SL(n,ℝ) via predicate surface "isMaximalCompactSubgroupOf" NERFINISHED ⓘ |
| SU(3) |
special linear group SL(n,C)
ⓘ
surface form:
SL(3,ℂ)
|
| Spin(2,d) | Spin(2)\times Spin(d) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
| orthogonal group O(n) | GL(n,R) via predicate surface "isMaximalCompactSubgroupOf" NERFINISHED ⓘ |
| orthogonal group O(n+1,2) | O(n+1)×O(2) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |