|
gptkbp:instanceOf
|
gptkb:group_of_people
gptkb:Lie_group
|
|
gptkbp:actsOn
|
gptkb:toric_varieties
|
|
gptkbp:appearsIn
|
theory of principal bundles
theory of abelian varieties
theory of algebraic tori
theory of compact Lie groups
theory of fiber bundles
theory of group actions
theory of homogeneous spaces
|
|
gptkbp:automorphismGroup
|
gptkb:GL(n,Z)
|
|
gptkbp:centralTo
|
itself
|
|
gptkbp:dimensions
|
n (for n-dimensional torus group)
|
|
gptkbp:example
|
gptkb:circle_group_S^1
gptkb:2-torus_T^2
gptkb:n-torus_T^n
|
|
gptkbp:fundamentalGroup
|
Z^n
|
|
gptkbp:has_Haar_measure
|
yes
|
|
gptkbp:heldBy
|
gptkb:Lie_group
gptkb:commutative_group
connected Lie group
complex Lie group (in some contexts)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
torus group
|
|
gptkbp:isomorphicTo
|
gptkb:R^n/Z^n
(S^1)^n
|
|
gptkbp:Lie_algebra
|
R^n
|
|
gptkbp:maximal_torus
|
appears in classification of compact Lie groups
|
|
gptkbp:notation
|
T^n
|
|
gptkbp:relatedTo
|
gptkb:Pontryagin_duality
gptkb:Fourier_analysis_on_tori
gptkb:lattice_in_R^n
|
|
gptkbp:structure
|
gptkb:topology
gptkb:Riemannian_manifold
algebraic group (in some contexts)
|
|
gptkbp:universalCover
|
R^n
|
|
gptkbp:used_in
|
gptkb:algebraic_geometry
harmonic analysis
representation theory
symplectic geometry
|
|
gptkbp:bfsParent
|
gptkb:butter
|
|
gptkbp:bfsLayer
|
4
|