projective unitary group PU(n)

GPTKB entity

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
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	7
https://www.w3.org/2000/01/rdf-schema#label	projective unitary group PU(n)