special linear group SL(n, R)

URI: https://gptkb.org/entity/special_linear_group_SL(n,_R)
GPTKB entity
Statements (34)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:actsOn R^n
gptkbp:centralTo {I, -I} for n even
{I} for n odd
gptkbp:compact true
gptkbp:containsElement n x n real matrices with determinant 1
gptkbp:definedIn real numbers
gptkbp:dimensions n^2 - 1
gptkbp:hasConnection true
gptkbp:hasDeterminantMap det: SL(n, R) → 1
gptkbp:hasMaximalSubgroup gptkb:SO(n)
gptkbp:hasSubgroup gptkb:general_linear_group_GL(n,_R)
https://www.w3.org/2000/01/rdf-schema#label special linear group SL(n, R)
gptkbp:importantFor gptkb:algebraic_geometry
differential geometry
physics
representation theory
gptkbp:isAlgebraicGroup true
gptkbp:isMatrixGroup true
gptkbp:isNonAbelian true
gptkbp:isNotSimplyConnectedFor n > 2
gptkbp:isReductive true
gptkbp:isSemisimple true
gptkbp:isSimple n > 2
gptkbp:isSimpleConnectedFor n = 2
gptkbp:isSmoothManifold true
gptkbp:isTopologicalGroup true
gptkbp:Lie_algebra gptkb:sl(n,_R)
gptkbp:notation gptkb:SL(n,_R)
gptkbp:realForm gptkb:SL(n,_C)
gptkbp:universalCover true
gptkbp:bfsParent gptkb:Lie_group
gptkbp:bfsLayer 5