special linear group SL(n, C)

URI: https://gptkb.org/entity/special_linear_group_SL(n,_C)
GPTKB entity
Statements (33)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:actsOn complex vector space of dimension n
gptkbp:centralTo cyclic group of order n
gptkbp:compact true
gptkbp:containsElement n x n complex matrices with determinant 1
gptkbp:definedIn complex numbers
gptkbp:determinant 1
gptkbp:dimensions n^2 - 1
gptkbp:hasConnection true
gptkbp:hasSubgroup gptkb:general_linear_group_GL(n,_C)
gptkbp:hasTrivialDeterminant true
https://www.w3.org/2000/01/rdf-schema#label special linear group SL(n, C)
gptkbp:isAlgebraicGroup true
gptkbp:isChevalleyGroup true
gptkbp:isClassicalGroup true
gptkbp:isConnectedLieGroup true
gptkbp:isMatrixGroup true
gptkbp:isNonAbelian true
gptkbp:isPerfect true
gptkbp:isQuotientOf gptkb:projective_special_linear_group_PSL(n,_C)
gptkbp:isReductive true
gptkbp:isSemisimple true
gptkbp:isSimple true
gptkbp:Lie_algebra gptkb:sl(n,_C)
gptkbp:notation gptkb:SL(n,_C)
gptkbp:universalCover gptkb:projective_special_linear_group_PSL(n,_C)
gptkbp:usedIn gptkb:algebraic_geometry
gptkb:theoretical_physics
differential geometry
representation theory
gptkbp:bfsParent gptkb:special_unitary_group_SU(n)
gptkbp:bfsLayer 6