Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
real projective space
|
| gptkbp:centralTo |
{I} for n odd, {I, -I} for n even
|
| gptkbp:connects |
yes
|
| gptkbp:defines |
group of n×n real matrices with determinant 1
|
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:field |
real numbers
|
| gptkbp:fullName |
special linear group of degree n over the real numbers
|
| gptkbp:hasSubgroup |
gptkb:GL(n,R)
|
| https://www.w3.org/2000/01/rdf-schema#label |
sl(n,R)
|
| gptkbp:isSimple |
yes, for n > 2
|
| gptkbp:Lie_algebra |
sl(n,R) (Lie algebra)
|
| gptkbp:maximal_compact_subgroup |
gptkb:SO(n)
|
| gptkbp:non-compact |
yes
|
| gptkbp:notation |
SL(n,ℝ)
|
| gptkbp:real_rank |
n-1
|
| gptkbp:used_in |
differential geometry
physics representation theory algebraic groups |
| gptkbp:bfsParent |
gptkb:special_linear_group_SL(n,R)
|
| gptkbp:bfsLayer |
7
|