projective unitary group PU(n)

URI: https://gptkb.org/entity/projective_unitary_group_PU(n)
GPTKB entity
Statements (28)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:Lie_group
gptkbp:actsOn gptkb:complex_projective_space_CP^{n-1}
gptkbp:appearsIn gptkb:algebraic_geometry
differential geometry
quantum mechanics
representation theory
gptkbp:centerOfU(n) Z(U(n)) = {λI | λ ∈ U(1)}
gptkbp:compact true
gptkbp:definedIn PU(n) = U(n) / Z(U(n))
gptkbp:dimensions n^2 - 1
gptkbp:fundamentalGroup Z/nZ for n ≥ 2
gptkbp:hasConnection true
gptkbp:hasTrivialCenter true
https://www.w3.org/2000/01/rdf-schema#label projective unitary group PU(n)
gptkbp:isHomogeneousSpace U(n)/U(1)
gptkbp:isMaximalCompactSubgroupOf gptkb:PGL(n,_C)
gptkbp:isNonabelianFor n ≥ 2
gptkbp:isomorphicTo U(n)/U(1)
gptkbp:isQuotientOf gptkb:unitary_group_U(n)
center of U(n)
gptkbp:isSimple n ≥ 2
gptkbp:isSimpleLieGroupFor n ≥ 2
gptkbp:Lie_algebra su(n)/center
gptkbp:realForm gptkb:projective_general_linear_group_PGL(n,_C)
gptkbp:relatedTo gptkb:projective_linear_group_PGL(n,_C)
gptkbp:bfsParent gptkb:unitary_group_U(n)
gptkbp:bfsLayer 6