Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
ℝ^n
|
| gptkbp:centralTo |
{λI | λ^n = 1, λ ∈ ℝ}
|
| gptkbp:connects |
true
|
| gptkbp:definedIn |
the group of n×n real matrices with determinant 1
|
| gptkbp:determinant |
1
|
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:field |
ℝ
|
| gptkbp:fullName |
Special Linear Group of degree n over the real numbers
|
| gptkbp:hasMaximalSubgroup |
gptkb:SO(n)
|
| gptkbp:hasSubgroup |
GL(n, ℝ)
|
| https://www.w3.org/2000/01/rdf-schema#label |
SL(n, ℝ)
|
| gptkbp:identityElement |
n×n identity matrix
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isSimple |
n ≥ 2
true for n ≥ 2 |
| gptkbp:Lie_algebra |
sl(n, ℝ)
|
| gptkbp:nonCompact |
true
|
| gptkbp:notation |
gptkb:SL(n,_ℝ)
|
| gptkbp:realForm |
gptkb:SL(n,_ℂ)
|
| gptkbp:relatedGroup |
matrix multiplication
|
| gptkbp:type |
non-abelian group
|
| gptkbp:usedIn |
differential geometry
physics representation theory algebraic groups |
| gptkbp:bfsParent |
gptkb:orthogonal_group
|
| gptkbp:bfsLayer |
5
|