definition A.326 Symmetrization

open in the book · appendices/A-long-proofs.tex:15993 · p. 2950

ground object -- no derivation owed

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 definition 14.5 Universal enveloping algebra ¶ ↺

Supports

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 ¶

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`	→	Symmetric algebra and symbol	declared	appendices/A-long-proofs.tex:16005
`depends_on`	→	Universal enveloping algebra	declared	appendices/A-long-proofs.tex:16005
`depends_on`	←	Symmetrization is an isomorphism of $\mathfrak{g}$-modules	declared	appendices/A-long-proofs.tex:16021