proposition 15.55 Completeness fails for $k\ge3$

Rests on

• depends_on example 15.57 $k=2$ recovers the Killing form ¶
  • depends_on theorem 15.51 Factorisation of invariant forms ¶
    • depends_on definition 15.3 Tensor product Lie algebra ¶
    • proves proof ch:13-lie-algebra-expansions@proof-30 ¶
  • depends_on theorem 15.10 Factorisation of the Killing form ¶
    • depends_on definition 15.3 Tensor product Lie algebra ¶ ↺
    • depends_on definition 15.9 Trace form of an algebra ¶
    • proves proof ch:13-lie-algebra-expansions@proof-5 ¶
• depends_on theorem 15.53 The factorised forms are exactly the balanced ones ¶
  • depends_on definition 15.52 Balanced form ¶
    • depends_on definition 15.3 Tensor product Lie algebra ¶ ↺
  • depends_on lemma 15.50 Every $k$-trace comes from a linear functional ¶
    • depends_on definition 15.49 $k$-trace ¶
    • proves proof ch:13-lie-algebra-expansions@proof-29 ¶
  • depends_on theorem 15.51 Factorisation of invariant forms ¶ ↺
  • proves proof ch:13-lie-algebra-expansions@proof-31 ¶
• depends_on theorem 15.51 Factorisation of invariant forms ¶ ↺
• proves proof ch:13-lie-algebra-expansions@proof-32 ¶

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