Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
differential geometry
harmonic analysis representation theory |
| gptkbp:class |
isomorphic to R^n × T^m × F (F finite Abelian group)
|
| gptkbp:compact |
isomorphic to torus × finite Abelian group
|
| gptkbp:connectedComponent |
isomorphic to R^n × T^m
|
| gptkbp:defines |
Lie groups whose group operation is commutative
|
| gptkbp:dimensions |
can be any non-negative integer
|
| gptkbp:example |
gptkb:n-dimensional_torus
gptkb:circle_group real numbers under addition |
| gptkbp:finite-dimensional |
yes
|
| https://www.w3.org/2000/01/rdf-schema#label |
Abelian Lie groups
|
| gptkbp:property |
all elements commute
|
| gptkbp:relatedTo |
gptkb:Pontryagin_duality
gptkb:locally_compact_Abelian_groups |
| gptkbp:simply_connected |
isomorphic to R^n
|
| gptkbp:structure |
isomorphic to product of Euclidean space and torus
|
| gptkbp:subclassOf |
gptkb:Lie_group
Abelian group |
| gptkbp:bfsParent |
gptkb:Lie_group
gptkb:Lie_groups |
| gptkbp:bfsLayer |
5
|