lemma A.349 Lifting generators through the filtration

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 proposition A.348 Symmetrization identifies the invariants ¶
  • depends_on definition A.325 Symmetric algebra and symbol ¶ ↺
  • 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 ¶
• proves proof app:A-long-proofs@proof-215 ¶

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