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.
Observed surface forms (3)
- classical group ×1
- rank-one Lie group ×1
- simple Lie group (for n ≥ 2) ×1
Instances (10)
-
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) via concept surface "classical group"
-
special unitary group SU(n)
via concept surface "simple Lie group (for n ≥ 2)"
surface form: SU(n)
-
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)