theorem A.319 Poincaré–Birkhoff–Witt

open in the book · appendices/A-long-proofs.tex:15650 · p. 2947

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 ¶
depends_on equation 14.12 eq:lie-uea-relations ¶
proves proof app:A-long-proofs@proof-198 ¶

Supports

depends_on corollary A.328 The Casimir elements are not accidentally zero ¶
depends_on definition A.325 Symmetric algebra and symbol ¶
- depends_on corollary A.328 The Casimir elements are not accidentally zero ¶ ↺
- depends_on definition A.326 Symmetrization ¶
  - depends_on proposition A.327 Symmetrization is an isomorphism of $\mathfrak{g}$-modules ¶
    - depends_on proposition A.348 Symmetrization identifies the invariants ¶
      - depends_on lemma A.349 Lifting generators through the filtration ¶
- depends_on lemma A.349 Lifting generators through the filtration ¶ ↺
- depends_on proposition A.327 Symmetrization is an isomorphism of $\mathfrak{g}$-modules ¶ ↺
- depends_on proposition A.348 Symmetrization identifies the invariants ¶ ↺
depends_on proposition A.327 Symmetrization is an isomorphism of $\mathfrak{g}$-modules ¶ ↺

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	appendices/A-long-proofs.tex:15662
`depends_on`	→	eq:lie-uea-relations	declared	appendices/A-long-proofs.tex:15662
`depends_on`	←	The Casimir elements are not accidentally zero	declared	appendices/A-long-proofs.tex:16081
`depends_on`	←	Symmetric algebra and symbol	declared	appendices/A-long-proofs.tex:15990
`depends_on`	←	Symmetrization is an isomorphism of $\mathfrak{g}$-modules	declared	appendices/A-long-proofs.tex:16021
`proves`	←	app:A-long-proofs@proof-198	declared	appendices/A-long-proofs.tex:15919