general linear group GL(n+1,C)

URI: https://gptkb.org/entity/general_linear_group_GL(n+1,C)
GPTKB entity
Statements (34)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:actsOn complex vector space of dimension n+1
gptkbp:centralTo scalar matrices
gptkbp:contains special linear group SL(n+1,C)
gptkbp:containsElement invertible (n+1)x(n+1) complex matrices
gptkbp:definedIn complex numbers
gptkbp:dimensions (n+1)^2
gptkbp:hasConnection true
gptkbp:hasDeterminantHomomorphism true
gptkbp:hasSubgroup orthogonal group O(n+1,C)
special linear group SL(n+1,C)
unitary group U(n+1)
https://www.w3.org/2000/01/rdf-schema#label general linear group GL(n+1,C)
gptkbp:identityElement identity matrix
gptkbp:isAlgebraicGroup true
gptkbp:isClassicalGroup true
gptkbp:isMatrixGroup true
gptkbp:isNonAbelian true
gptkbp:isParabolicSubgroupOf itself
gptkbp:isQuotientOf projective general linear group PGL(n+1,C)
gptkbp:isReductive true
gptkbp:isSimple false
gptkbp:isTopologicalGroup true
gptkbp:notation GL(n+1,C)
gptkbp:operator matrix multiplication
gptkbp:realForm general linear group GL(n+1,R)
gptkbp:usedIn gptkb:algebraic_geometry
differential geometry
number theory
physics
representation theory
gptkbp:bfsParent gptkb:general_linear_group_GL(n,C)
gptkbp:bfsLayer 7