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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| hasMaximalTorus | 3 |
| isMaximalTorusIn | 2 |
| maximalTorus canonical | 2 |
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: maximalTorus
Generated description
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.
Sample triples (7)
| Subject | Object |
|---|---|
|
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" ⓘ |
| U(1) | U(n) via predicate surface "isMaximalTorusIn" ⓘ |
| U(1) | SU(2) via predicate surface "isMaximalTorusIn" ⓘ |
|
special unitary group SU(n)
surface form:
SU(n)
|
diagonal unitary matrices with determinant 1 ⓘ |
|
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" ⓘ |