adjoint action of the Lie algebra
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
The adjoint action of a Lie algebra g is the linear map ad: g → End(g) defined by ad(x)(y) = [x, y] for x, y in g.
|
| gptkbp:field |
gptkb:Lie_theory
gptkb:mathematics representation theory |
| https://www.w3.org/2000/01/rdf-schema#label |
adjoint action of the Lie algebra
|
| gptkbp:mappedFrom |
gptkb:Lie_group
|
| gptkbp:mapType |
endomorphisms of the Lie algebra
|
| gptkbp:notation |
ad
|
| gptkbp:property |
ad is a Lie algebra homomorphism
kernel of ad is the center of the Lie algebra |
| gptkbp:relatedTo |
gptkb:Lie_group
adjoint representation |
| gptkbp:usedIn |
classification of Lie algebras
structure theory of Lie algebras study of derivations |
| gptkbp:bfsParent |
gptkb:Casimir_operator
|
| gptkbp:bfsLayer |
6
|