Universal enveloping algebra
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:built |
gptkb:Poincaré–Birkhoff–Witt_theorem
|
| gptkbp:category |
gptkb:Lie_theory
gptkb:algebra |
| gptkbp:defines |
An associative algebra that contains a given Lie algebra and satisfies a universal property with respect to Lie algebra homomorphisms.
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:hasSubfield |
abstract algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Universal enveloping algebra
|
| gptkbp:introduced |
gptkb:Nathan_Jacobson
|
| gptkbp:introducedIn |
1940s
|
| gptkbp:notation |
U(g)
|
| gptkbp:property |
gptkb:associative_algebra
contains Lie algebra as subspace satisfies universal property |
| gptkbp:relatedTo |
gptkb:Lie_group
|
| gptkbp:seeAlso |
gptkb:Lie_group
enveloping algebra |
| gptkbp:usedIn |
differential geometry
mathematical physics representation theory quantum groups |
| gptkbp:bfsParent |
gptkb:Enveloping_Algebras
|
| gptkbp:bfsLayer |
7
|