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.
Observed surface forms (13)
- 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 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
Instances (26)
- Cartan decomposition
- Lie algebra representation via concept surface "representation theory concept"
- Onsager algebra via concept surface "Lie algebra"
- SL(2,C) via concept surface "complex Lie group"
- SU(3) via concept surface "semisimple Lie group"
- Clebsch–Gordan coefficients via concept surface "representation theory concept"
- affine Lie algebras via concept surface "infinite-dimensional Lie algebra"
-
rotation group SU(2)
via concept surface "semisimple Lie group"
surface form: SU(2)
- Weyl denominator via concept surface "object in Lie theory"
- Heisenberg Lie algebra via concept surface "Lie algebra"
- Borel subalgebras via concept surface "notion in Lie theory"
- Iwasawa decomposition via concept surface "decomposition in Lie theory"
- Verma module via concept surface "representation theory concept"
-
special unitary group SU(n)
via concept surface "semisimple Lie group"
surface form: SU(n)
-
special linear group SL(n,R)
via concept surface "Lie algebra"
surface form: sl(n,ℝ)
-
general linear group GL(n,C)
via concept surface "complex Lie group"
surface form: GL(n,ℂ)
-
special linear group SL(n,C)
via concept surface "complex Lie group"
surface form: SL(n,ℂ)
- SL(2,ℤ) via concept surface "lattice in Lie group"
- PSL(2,ℝ) via concept surface "semisimple Lie group"
- SL(2,R) via concept surface "semisimple Lie group"
- Langlands dual group via concept surface "concept in representation theory"
- Harish-Chandra projection via concept surface "tool in Lie theory"
- Langlands classification via concept surface "concept in representation theory"
-
PSL(2,\mathbb{C})
via concept surface "complex Lie group"
surface form: PSL(2,ℂ)
- Jordan–Chevalley decomposition via concept surface "concept in representation theory"
- non-Abelian Berry connection via concept surface "concept in geometric phase theory"