theorem 14.7 Poincaré–Birkhoff–Witt

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:313 · p. 545

Rests on

depends_on definition 14.5 Universal enveloping algebra ¶
- depends_on equation 14.5 eq:lie-structconst ¶
  - step_from equation 14.4 eq:lie-gengrlie ¶
    - step_from equation 14.3 eq:lie-generators ¶
    - step_from equation 14.2 eq:lie-varincor ¶
proves proof ch:12-lie-groups-fibre-bundles@prooflink-1 ¶

Supports

depends_on lemma 14.87 A rescaled Casimir stays central ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Universal enveloping algebra	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:319
`depends_on`	←	A rescaled Casimir stays central	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:3803
`proves`	←	ch:12-lie-groups-fibre-bundles@prooflink-1	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:326