hasLieAlgebraDimension
P63682
predicate
Indicates that an algebraic structure is associated with a Lie algebra having a specified vector-space dimension.
All labels observed (5)
| Label | Occurrences |
|---|---|
| LieAlgebraDimension | 4 |
| hasLieAlgebraDimension canonical | 3 |
| dimensionOfHolonomyGroup | 1 |
| hasComplexLieAlgebraDimension | 1 |
| hasRealLieAlgebraDimension | 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: hasLieAlgebraDimension
Generated description
Indicates that an algebraic structure is associated with a Lie algebra having a specified vector-space dimension.
Sample triples (10)
| Subject | Object |
|---|---|
| E(n) | n(n+1)/2 ⓘ |
| SU(3) | 8 ⓘ |
|
rotation group SO(3)
surface form:
SO(3)
|
3 via predicate surface "LieAlgebraDimension" ⓘ |
| SL(2,C) | 6 via predicate surface "hasRealLieAlgebraDimension" ⓘ |
| SL(2,C) | 3 via predicate surface "hasComplexLieAlgebraDimension" ⓘ |
| Calabi–Yau metric | n^2-1 via predicate surface "dimensionOfHolonomyGroup" ⓘ |
| U(1) | 1 ⓘ |
|
special unitary group SU(n)
surface form:
SU(n)
|
n² − 1 via predicate surface "LieAlgebraDimension" ⓘ |
|
general linear group GL(n,R)
surface form:
GL(n,ℝ)
|
n^2 via predicate surface "LieAlgebraDimension" ⓘ |
| SL(2,R) | 3 via predicate surface "LieAlgebraDimension" ⓘ |