general linear group GL(n,C)

URI: https://gptkb.org/entity/general_linear_group_GL(n,C)
GPTKB entity
Statements (46)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:actsOn complex vector space of dimension n
gptkbp:centralTo scalar matrices
gptkbp:compact true
gptkbp:containsElement invertible n x n complex matrices
gptkbp:definedIn complex numbers
gptkbp:dimensions n^2
gptkbp:field C
gptkbp:fundamentalGroup Z
gptkbp:hasConnection true
gptkbp:hasDeterminantHomomorphism true
gptkbp:hasDeterminantMap gptkb:C*
gptkbp:hasMaximalSubgroup gptkb:unitary_group_U(n)
gptkbp:hasMaximalTorus diagonal matrices
gptkbp:hasSubgroup gptkb:special_linear_group_SL(n,C)
gptkb:general_linear_group_GL(n+1,C)
https://www.w3.org/2000/01/rdf-schema#label general linear group GL(n,C)
gptkbp:identityElement identity matrix
gptkbp:isAlgebraicGroup true
gptkbp:isClassicalGroup true
gptkbp:isComplexLieGroup true
gptkbp:isDenseIn M(n,C)
gptkbp:isHomogeneousSpace false
gptkbp:isMatrixGroup true
gptkbp:isNonAbelian true
gptkbp:isNonSimpleFor n>1
gptkbp:isNotSimplyConnected true
gptkbp:isOpenSubsetOf M(n,C)
gptkbp:isParabolicSubgroupOf itself
gptkbp:isQuotientOf gptkb:projective_general_linear_group_PGL(n,C)
gptkbp:isReductive true
gptkbp:isSimple false
n=1
gptkbp:isSmoothManifold true
gptkbp:isSplitGroup true
gptkbp:isTopologicalGroup true
gptkbp:isZariskiOpen true
gptkbp:Lie_algebra gptkb:gl(n,C)
gptkbp:notation gptkb:GL(n,C)
gptkb:GL_n(C)
gptkbp:relatedGroup matrix multiplication
gptkbp:relatedTo gptkb:automorphism_group_of_C^n
gptkbp:universalCover itself
gptkbp:bfsParent gptkb:unitary_group_U(n)
gptkbp:bfsLayer 6