special linear Lie algebra over the real numbers
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Lie_group
|
| gptkbp:alsoKnownAs |
gptkb:sl(n,_R)
|
| gptkbp:application |
gptkb:theoretical_physics
differential geometry representation theory |
| gptkbp:basisFor |
matrices with one 1, one -1, rest 0
|
| gptkbp:centralTo |
trivial (zero matrix)
|
| gptkbp:consistsOf |
n x n real matrices with trace zero
|
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:field |
real numbers
|
| gptkbp:generation |
elementary matrices with trace zero
|
| https://www.w3.org/2000/01/rdf-schema#label |
special linear Lie algebra over the real numbers
|
| gptkbp:isSimple |
true (for n > 1)
|
| gptkbp:notation |
gptkb:sl(n,_R)
|
| gptkbp:rank |
n-1
|
| gptkbp:realForm |
complex special linear Lie algebra sl(n, C)
|
| gptkbp:relatedGroup |
special linear group over the real numbers
|
| gptkbp:structureConstants |
given by commutator of matrices
|
| gptkbp:subclassOf |
general linear Lie algebra over the real numbers
|
| gptkbp:type |
gptkb:classical_Lie_algebra
A_{n-1} |
| gptkbp:bfsParent |
gptkb:sl(n,_R)
|
| gptkbp:bfsLayer |
7
|