quotientedBy
P97909
predicate
Indicates that one structure or set is formed from another by identifying elements according to an equivalence relation or partition, yielding a quotient.
All labels observed (16)
| Label | Occurrences |
|---|---|
| quotientBy | 7 |
| quotientOf | 6 |
| quotientsOut | 4 |
| quotientByCenterIs | 3 |
| quotientDescription | 3 |
| quotientedBy canonical | 3 |
| quotientByCenter | 2 |
| quotientGives | 2 |
| constructedAsQuotientOf | 1 |
| constructedByQuotienting | 1 |
| hasQuotientBy | 1 |
| quotientByA5 | 1 |
| quotientByPrincipalDivisors | 1 |
| quotientBySubgroup | 1 |
| quotientInterpretedAs | 1 |
| quotientIsomorphicTo | 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: quotientedBy
Generated description
Indicates that one structure or set is formed from another by identifying elements according to an equivalence relation or partition, yielding a quotient.
Sample triples (38)
| Subject | Object |
|---|---|
| Milnor K-theory | Steinberg relation {a,1−a}=0 for a,1−a≠0 ⓘ |
|
rotation group SU(2)
surface form:
SU(2)
|
SO(3) via predicate surface "quotientByCenterIs" NERFINISHED ⓘ |
|
Kummer surfaces
surface form:
Kummer surface
|
abelian surface by the involution x ↦ −x via predicate surface "quotientOf" ⓘ |
| ISO(n) | R^n via predicate surface "quotientBy" ⓘ |
| ISO(n) | O(n) via predicate surface "quotientIsomorphicTo" ⓘ |
| affine group of R^n | (affine group of R^n, translation subgroup R^n) ≅ GL(n,R) via predicate surface "hasQuotientBy" ⓘ |
|
universal enveloping algebras
surface form:
universal enveloping algebra
|
tensor algebra by the ideal generated by x⊗y − y⊗x − [x,y] via predicate surface "constructedByQuotienting" ⓘ |
|
Dolbeault cohomology classes
surface form:
Dolbeault cohomology class
|
space of ∂̄-closed (p,q)-forms by ∂̄-exact (p,q)-forms via predicate surface "quotientOf" ⓘ |
|
special linear group SL(n,R)
surface form:
SL(2,ℝ)
|
{±I} is PSL(2,ℝ) via predicate surface "quotientBy" ⓘ |
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
PGL(n,ℂ) via predicate surface "quotientByCenter" ⓘ |
| Outer space (Culler–Vogtmann Outer space) | Out(F_n) gives moduli space of metric graphs of rank n via predicate surface "quotientBy" NERFINISHED ⓘ |
| Culler–Vogtmann Outer space | Out(F_n) via predicate surface "quotientBy" NERFINISHED ⓘ |
| Culler–Vogtmann Outer space | analogue of moduli space of graphs via predicate surface "quotientInterpretedAs" ⓘ |
| PSL(2,ℤ/Nℤ) | center of SL(2,ℤ/Nℤ) ⓘ |
| PSL(2,ℤ/Nℤ) | {±I} when 2 is invertible in ℤ/Nℤ ⓘ |
| SL(2,ℤ) | PSL(2,ℤ) via predicate surface "quotientByCenterIs" ⓘ |
| PSL(2,ℝ) | SL(2,ℝ) via predicate surface "quotientOf" NERFINISHED ⓘ |
| PSL(2,ℝ) | {±I} via predicate surface "quotientBy" ⓘ |
| SL(2,R) | PSL(2,R) via predicate surface "quotientByCenter" NERFINISHED ⓘ |
| Witt group of quadratic forms | hyperbolic quadratic forms via predicate surface "quotientsOut" ⓘ |
| Witt group of quadratic forms | metabolic quadratic forms via predicate surface "quotientsOut" ⓘ |
| idèle class group | ideal class group via predicate surface "quotientBySubgroup" ⓘ |
| Cartier divisor | Picard group via predicate surface "quotientByPrincipalDivisors" NERFINISHED ⓘ |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
SL(2,ℂ) via predicate surface "quotientOf" ⓘ |
| SL(2,7) | PSL(2,7) via predicate surface "quotientByCenterIs" NERFINISHED ⓘ |
| PGL(2,7) | GL(2,7) via predicate surface "quotientOf" NERFINISHED ⓘ |
| S5 | A5 via predicate surface "quotientBy" ⓘ |
| symmetric group S5 | cyclic group of order 2 via predicate surface "quotientByA5" ⓘ |
| Teichmüller space | mapping class group via predicate surface "quotientBy" NERFINISHED ⓘ |
| Teichmüller space | moduli space of curves via predicate surface "quotientGives" ⓘ |
| Teichmüller space | moduli space of Riemann surfaces via predicate surface "quotientGives" NERFINISHED ⓘ |
| Temperley–Lieb algebra | Hecke algebra of type A via predicate surface "quotientOf" NERFINISHED ⓘ |
| Grassmann manifolds | Gr(k,n) ≅ GL(n)/P where P is a parabolic subgroup via predicate surface "quotientDescription" ⓘ |
| Grassmann manifolds | Gr(k,n) ≅ O(n)/(O(k) × O(n − k)) via predicate surface "quotientDescription" ⓘ |
| Grassmann manifolds | Gr(k,n) ≅ U(n)/(U(k) × U(n − k)) via predicate surface "quotientDescription" ⓘ |
|
Whitehead groups
surface form:
Whitehead group
|
K1(Z[G]) via predicate surface "constructedAsQuotientOf" ⓘ |
|
Whitehead groups
surface form:
Whitehead group
|
±G via predicate surface "quotientsOut" ⓘ |
|
Whitehead groups
surface form:
Whitehead group
|
image of trivial units in Z[G] via predicate surface "quotientsOut" ⓘ |