|
gptkbp:instanceOf
|
gptkb:mathematical_concept
gptkb:Lie_group
|
|
gptkbp:example
|
gptkb:special_linear_group_SL(n,_R)
gptkb:symplectic_group_Sp(n)
gptkb:orthogonal_group_O(n)
gptkb:unitary_group_U(n)
|
|
gptkbp:hasApplication
|
chemistry
control theory
engineering
physics
robotics
|
|
gptkbp:hasProperty
|
finite-dimensional
locally compact
second-countable
group operations are smooth
Hausdorff topology
analytic group operations
|
|
gptkbp:heldBy
|
gptkb:Riemannian_manifold
gptkb:Lie_group
closed subgroup of GL(n, C)
group of matrices
subgroup of general linear group
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
linear Lie group
|
|
gptkbp:is_defined_over
|
quaternions
complex numbers
real numbers
|
|
gptkbp:is_subset_of
|
gptkb:GL(n,_F)
|
|
gptkbp:Lie_algebra
|
matrix Lie algebra
|
|
gptkbp:namedFor
|
gptkb:Élie_Cartan
|
|
gptkbp:relatedTo
|
gptkb:algebraic_geometry
gptkb:group_of_people
gptkb:topology
gptkb:knowledge_representation
gptkb:Lie_group
gptkb:Baker–Campbell–Hausdorff_formula
Lie group action
Lie subgroup
exponential map
homomorphism
representation theory of Lie groups
structure theory
classification of Lie groups
homogeneous space
Lie group homomorphism
|
|
gptkbp:structure
|
locally Euclidean
|
|
gptkbp:studiedBy
|
differential geometry
representation theory
|
|
gptkbp:bfsParent
|
gptkb:Lie_group
|
|
gptkbp:bfsLayer
|
5
|