concept in Lie theory
C18641
concept
A concept in Lie theory is an abstract mathematical construct—such as a Lie group, Lie algebra, or representation—that captures continuous symmetries and their algebraic and geometric properties.
All labels observed (14)
| Label | Occurrences |
|---|---|
| semisimple Lie group | 7 |
| Lie algebra | 4 |
| complex Lie group | 4 |
| concept in representation theory | 3 |
| representation theory concept | 3 |
| infinite-dimensional Lie algebra | 2 |
| Kac–Moody algebra | 1 |
| concept in Lie theory canonical | 1 |
| concept in geometric phase theory | 1 |
| decomposition in Lie theory | 1 |
| lattice in Lie group | 1 |
| notion in Lie theory | 1 |
| object in Lie theory | 1 |
| tool in Lie theory | 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: concept in Lie theory
Generated description
A concept in Lie theory is an abstract mathematical construct—such as a Lie group, Lie algebra, or representation—that captures continuous symmetries and their algebraic and geometric properties.
Instances (26)
| Instance | Via concept surface |
|---|---|
| Cartan decomposition | — |
| Lie algebra representation | representation theory concept |
| Onsager algebra | Lie algebra |
| SL(2,C) | complex Lie group |
| SU(3) | semisimple Lie group |
| Clebsch–Gordan coefficients | representation theory concept |
| affine Lie algebras | infinite-dimensional Lie algebra |
|
rotation group SU(2)
surface form:
SU(2)
|
semisimple Lie group |
| Weyl denominator | object in Lie theory |
| Heisenberg Lie algebra | Lie algebra |
| Borel subalgebras | notion in Lie theory |
| Iwasawa decomposition | decomposition in Lie theory |
| Verma module | representation theory concept |
|
special unitary group SU(n)
surface form:
SU(n)
|
semisimple Lie group |
|
special linear group SL(n,R)
surface form:
sl(n,ℝ)
|
Lie algebra |
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
complex Lie group |
|
special linear group SL(n,C)
surface form:
SL(n,ℂ)
|
complex Lie group |
| SL(2,ℤ) | lattice in Lie group |
| PSL(2,ℝ) | semisimple Lie group |
| SL(2,R) | semisimple Lie group |
| Langlands dual group | concept in representation theory |
| Harish-Chandra projection | tool in Lie theory |
| Langlands classification | concept in representation theory |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
complex Lie group |
| Jordan–Chevalley decomposition | concept in representation theory |
| non-Abelian Berry connection | concept in geometric phase theory |