simple Lie group
C22583
concept
A simple Lie group is a connected non-abelian Lie group whose Lie algebra is simple, meaning it has no nontrivial proper ideals and is not a direct sum of smaller Lie algebras.
All labels observed (4)
| Label | Occurrences |
|---|---|
| simple Lie group canonical | 8 |
| classical group | 1 |
| rank-one Lie group | 1 |
| simple Lie group (for n ≥ 2) | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: simple Lie group
Generated description
A simple Lie group is a connected non-abelian Lie group whose Lie algebra is simple, meaning it has no nontrivial proper ideals and is not a direct sum of smaller Lie algebras.
Instances (10)
| Instance | Via concept surface |
|---|---|
|
rotation group SO(3)
surface form:
SO(3)
|
— |
| SL(2,C) | — |
| SU(3) | — |
|
rotation group SU(2)
surface form:
SU(2)
|
— |
| orthogonal group O(n) | classical group |
|
special unitary group SU(n)
surface form:
SU(n)
|
simple Lie group (for n ≥ 2) |
|
special linear group SL(n,C)
surface form:
SL(n,ℂ)
|
— |
| PSL(2,ℝ) | — |
| SL(2,R) | — |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
— |