|
gptkbp:instanceOf
|
gptkb:algebraic_geometry
gptkb:mathematical_concept
gptkb:Riemannian_manifold
projective plane
|
|
gptkbp:alsoKnownAs
|
gptkb:octonionic_projective_plane
|
|
gptkbp:alternativeName
|
Cayley_plane
|
|
gptkbp:application
|
gptkb:quantum_field_theory
gptkb:Schubert_calculus
coding theory
moduli spaces
|
|
gptkbp:automorphismGroup
|
gptkb:F4
|
|
gptkbp:category
|
homogeneous space
|
|
gptkbp:compact
|
true
|
|
gptkbp:definedIn
|
gptkb:octonions
|
|
gptkbp:defines
|
the space of all k-dimensional linear subspaces of an n-dimensional vector space
|
|
gptkbp:dimensionFormula
|
k(n-k)
|
|
gptkbp:dimensions
|
16
|
|
gptkbp:Euler_characteristic
|
3
|
|
gptkbp:field
|
gptkb:mathematics
|
|
gptkbp:hasBettiNumber
|
0
1
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasSpecialCase
|
gptkb:geometry
|
|
gptkbp:hasSubfield
|
gptkb:algebraic_geometry
differential geometry
representation theory
|
|
gptkbp:homogeneousSpaceOf
|
gptkb:general_linear_group
orthogonal group
|
|
gptkbp:isExceptional
|
true
|
|
gptkbp:isHomogeneousSpaceOf
|
gptkb:F4
|
|
gptkbp:isProjectivePlaneOver
|
gptkb:octonions
|
|
gptkbp:isQuotientOf
|
gptkb:F4/Spin(9)
|
|
gptkbp:isSymmetricSpace
|
true
|
|
gptkbp:namedAfter
|
gptkb:Hermann_Grassmann
|
|
gptkbp:notation
|
Gr(k, n)
|
|
gptkbp:relatedConcept
|
gptkb:Plücker_coordinates
gptkb:Plücker_embedding
gptkb:Schubert_cell
gptkb:Stiefel_manifold
flag variety
|
|
gptkbp:relatedTo
|
gptkb:F4_group
gptkb:geometry
gptkb:Moufang_plane
gptkb:exceptional_Lie_groups
gptkb:octonions
projective planes over division algebras
|
|
gptkbp:structure
|
gptkb:algebraic_geometry
gptkb:Riemannian_manifold
Kähler manifold
real manifold
|
|
gptkbp:symbol
|
OP^2
|
|
gptkbp:usedIn
|
gptkb:machine_learning
gptkb:signal_processing
gptkb:topology
gptkb:integral_geometry
gptkb:string_theory
gptkb:cluster_algebras
gptkb:mirror_symmetry
computer vision
control theory
data analysis
integrable systems
mathematical physics
statistics
twistor theory
combinatorics
random matrix theory
algebraic combinatorics
enumerative geometry
geometric representation theory
moduli theory
|
|
gptkbp:bfsParent
|
gptkb:geometry
|
|
gptkbp:bfsLayer
|
4
|