maximal torus in a connected Lie group
GPTKB entity
Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:centralizer_equals |
itself
|
| gptkbp:dimension_equals |
rank of the Lie group
|
| gptkbp:every_element_is_contained_in |
some maximal torus (for compact Lie groups)
|
| gptkbp:example_in_SO(3) |
rotations about a fixed axis
|
| gptkbp:example_in_SU(n) |
diagonal matrices with determinant 1
|
| gptkbp:exists_in_every |
connected compact Lie group
|
| gptkbp:heldBy |
gptkb:butter
gptkb:maximal_torus Lie subgroup subfamily compact, connected, abelian subgroup |
| https://www.w3.org/2000/01/rdf-schema#label |
maximal torus in a connected Lie group
|
| gptkbp:is_maximal_with_respect_to |
inclusion among tori
|
| gptkbp:is_unique_up_to |
conjugation
|
| gptkbp:normalizer_modulo_itself_is |
gptkb:Weyl_group
|
| gptkbp:relatedTo |
Cartan subalgebra
|
| gptkbp:used_in |
representation theory
structure theory of Lie groups |
| gptkbp:bfsParent |
gptkb:Cartan_subgroup
|
| gptkbp:bfsLayer |
6
|