hasMaximalCompactSubgroupOf
P78099
predicate
Indicates that one mathematical group is the maximal compact subgroup contained within another group.
All labels observed (4)
| Label | Occurrences |
|---|---|
| hasMaximalCompactSubgroup | 9 |
| isMaximalCompactSubgroupOf | 2 |
| maximalCompactSubgroup | 2 |
| hasMaximalCompactSubgroupOf canonical | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: hasMaximalCompactSubgroupOf
Generated description
Indicates that one mathematical group is the maximal compact subgroup contained within another group.
Sample triples (14)
| Subject | Object |
|---|---|
| SU(3) |
SL(3,ℂ)
ⓘ
linked to:
special linear group SL(n,C)
|
| SL(2,C) |
SU(2)
via predicate surface "hasMaximalCompactSubgroup"
ⓘ
linked to:
rotation group SU(2)
|
| orthogonal group O(n) | GL(n,R) via predicate surface "isMaximalCompactSubgroupOf" NERFINISHED ⓘ |
|
SO(n)
linked to:
special orthogonal group SO(n)
|
SL(n,ℝ) via predicate surface "isMaximalCompactSubgroupOf" NERFINISHED ⓘ |
| orthogonal group O(n+1,2) | O(n+1)×O(2) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
|
GL(n,ℝ)
linked to:
general linear group GL(n,R)
|
O(n) via predicate surface "hasMaximalCompactSubgroup" ⓘ |
|
SL(n,ℝ)
linked to:
special linear group SL(n,R)
|
SO(n) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
|
SL(2,ℝ)
linked to:
special linear group SL(n,R)
|
SO(2) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
| SO(2,d-1) | SO(2)×SO(d-1) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
| Spin(2,d) | Spin(2)\times Spin(d) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
|
GL(n,ℂ)
linked to:
general linear group GL(n,C)
|
U(n) via predicate surface "maximalCompactSubgroup" NERFINISHED ⓘ |
| PSL(2,ℝ) | SO(2) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |
| SL(2,R) | SO(2) via predicate surface "maximalCompactSubgroup" NERFINISHED ⓘ |
|
PSL(2,ℂ)
linked to:
PSL(2,\mathbb{C})
|
PSU(2) via predicate surface "hasMaximalCompactSubgroup" NERFINISHED ⓘ |