Statements (49)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:actsOn |
real n-dimensional vector space
|
| gptkbp:centralTo |
{I, -I} for n even; {I} for n odd
|
| gptkbp:compact |
true (for n > 1)
|
| gptkbp:contains |
gptkb:SO(n)
|
| gptkbp:definedIn |
the group of n x n real matrices with determinant 1
|
| gptkbp:determinant |
1
|
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:field |
real numbers
|
| gptkbp:fullName |
Special Linear Group of degree n over the real numbers
|
| gptkbp:hasConnection |
true
false (for n > 1) |
| gptkbp:hasSubgroup |
gptkb:GL(n,R)
|
| https://www.w3.org/2000/01/rdf-schema#label |
SL(n,R)
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isNonAbelian |
true (for n > 1)
|
| gptkbp:isSemisimple |
true (for n > 1)
|
| gptkbp:isSimple |
true (for n > 2)
|
| gptkbp:isTopologically |
non-compact, connected Lie group
|
| gptkbp:Lie_algebra |
gptkb:sl(n,R)
|
| gptkbp:notation |
SL(n,ℝ)
|
| gptkbp:realForm |
gptkb:SL(n,C)
|
| gptkbp:universalCover |
true
|
| gptkbp:usedIn |
gptkb:Lie_theory
gptkb:algebraic_geometry gptkb:general_relativity gptkb:geometry gptkb:special_relativity gptkb:topology coding theory control theory cryptography differential geometry dynamical systems ergodic theory group theory mathematical physics modular forms number theory partial differential equations physics quantum mechanics representation theory algebraic groups automorphic forms symplectic geometry |
| gptkbp:bfsParent |
gptkb:special_linear_group_SL(n,R)
|
| gptkbp:bfsLayer |
7
|