Special Linear Group of degree n over the complex numbers
GPTKB entity
Statements (45)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:Lie_group |
| gptkbp:abbreviation |
gptkb:SL(n,_C)
|
| gptkbp:actsOn |
complex n-dimensional vector space
|
| gptkbp:centralTo |
set of scalar matrices with n-th roots of unity as entries
|
| gptkbp:compact |
true
|
| gptkbp:definedIn |
determinant = 1
group of n x n complex matrices with determinant 1 |
| gptkbp:dimensions |
n^2 - 1
|
| gptkbp:field |
complex numbers
|
| gptkbp:hasConnection |
true
|
| gptkbp:hasSubgroup |
General Linear Group of degree n over the complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
Special Linear Group of degree n over the complex numbers
|
| gptkbp:isAlgebraicGroup |
true
|
| gptkbp:isClosedSubgroupOf |
General Linear Group of degree n over the complex numbers
|
| gptkbp:isComplexLieGroup |
true
|
| gptkbp:isConnectedLieGroup |
true
|
| gptkbp:isHomomorphicImageOf |
Universal Covering Group of SL(n, C) (itself)
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isNonAbelian |
for n >= 2
|
| gptkbp:isNonAbelianSimpleGroup |
for n >= 2
|
| gptkbp:isNonCompactLieGroup |
true
|
| gptkbp:isReductive |
true
|
| gptkbp:isSemisimple |
true
|
| gptkbp:isSimple |
n >= 2
|
| gptkbp:isTransitiveOn |
complex n-dimensional vector space minus the origin
|
| gptkbp:Lie_algebra |
special linear Lie algebra sl(n, C)
|
| gptkbp:order |
infinite
|
| gptkbp:relatedTo |
Special Linear Group of degree n over the real numbers
General Linear Group GL(n, C) Projective Special Linear Group PSL(n, C) Special Orthogonal Group SO(n, C) Special Unitary Group SU(n) |
| gptkbp:universalCover |
itself
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:gauge_theory gptkb:theoretical_physics gptkb:topology differential geometry number theory particle physics quantum mechanics representation theory |
| gptkbp:bfsParent |
gptkb:SL(n,_ℂ)
|
| gptkbp:bfsLayer |
6
|