proposition A.348 Symmetrization identifies the invariants

open in the book · appendices/A-long-proofs.tex:16953 · p. 2960

Rests on

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 ¶
      - step_from equation 14.4 eq:lie-gengrlie ¶
- 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 lemma A.347 Central is the same as invariant ¶
- depends_on definition 14.8 Casimir element ¶
  - depends_on definition 14.5 Universal enveloping algebra ¶ ↺
- depends_on definition 14.5 Universal enveloping algebra ¶ ↺
- proves proof app:A-long-proofs@proof-213 ¶
depends_on proposition A.327 Symmetrization is an isomorphism of $\mathfrak{g}$-modules ¶
- depends_on definition A.326 Symmetrization ¶
  - depends_on definition A.325 Symmetric algebra and symbol ¶ ↺
  - 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 ¶
proves proof app:A-long-proofs@proof-214 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Symmetric algebra and symbol	declared	appendices/A-long-proofs.tex:16971
`depends_on`	→	Central is the same as invariant	declared	appendices/A-long-proofs.tex:16971
`depends_on`	→	Symmetrization is an isomorphism of $\mathfrak{g}$-modules	declared	appendices/A-long-proofs.tex:16971
`depends_on`	←	Lifting generators through the filtration	declared	appendices/A-long-proofs.tex:17012
`proves`	←	app:A-long-proofs@proof-214	declared	appendices/A-long-proofs.tex:16974