proposition A.327 Symmetrization is an isomorphism of $\mathfrak{g}$-modules

open in the book · appendices/A-long-proofs.tex:16008 · p. 2951

Rests on

depends_on definition A.326 Symmetrization ¶
- depends_on definition A.325 Symmetric algebra and symbol ¶
  - depends_on definition A.320 Filtration by degree ¶
    - depends_on definition 14.5 Universal enveloping algebra ¶
      - depends_on equation 14.5 eq:lie-structconst ¶
  - depends_on theorem A.319 Poincaré–Birkhoff–Witt ¶
    - depends_on definition 14.5 Universal enveloping algebra ¶ ↺
    - depends_on equation 14.12 eq:lie-uea-relations ¶
    - proves proof app:A-long-proofs@proof-198 ¶
- depends_on definition 14.5 Universal enveloping algebra ¶ ↺
depends_on definition A.325 Symmetric algebra and symbol ¶ ↺
depends_on theorem A.319 Poincaré–Birkhoff–Witt ¶ ↺
proves proof app:A-long-proofs@proof-199 ¶

Supports

depends_on proposition A.348 Symmetrization identifies the invariants ¶
- depends_on lemma A.349 Lifting generators through the filtration ¶

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`	→	Symmetrization	declared	appendices/A-long-proofs.tex:16021
`depends_on`	→	Symmetric algebra and symbol	declared	appendices/A-long-proofs.tex:16021
`depends_on`	→	Poincaré–Birkhoff–Witt	declared	appendices/A-long-proofs.tex:16021
`depends_on`	←	Symmetrization identifies the invariants	declared	appendices/A-long-proofs.tex:16971
`proves`	←	app:A-long-proofs@proof-199	declared	appendices/A-long-proofs.tex:16024