proposition 15.21 Resonance

Rests on

• depends_on definition 15.18 $\Z_{2}$-grading, symmetric coset ¶
• depends_on definition 15.20 Resonant subalgebra ¶
  • depends_on definition 15.18 $\Z_{2}$-grading, symmetric coset ¶ ↺
  • depends_on definition 15.14 Truncated polynomial algebra and Takiff algebra ¶
    • depends_on definition 15.3 Tensor product Lie algebra ¶
• depends_on proposition 15.15 Takiff brackets ¶
  • depends_on definition 15.14 Truncated polynomial algebra and Takiff algebra ¶ ↺
  • depends_on definition 15.3 Tensor product Lie algebra ¶ ↺
  • depends_on proposition 15.8 The radical of $A$ is solvable in $\mathfrak{g}_{A}$ ¶
    • depends_on definition 15.3 Tensor product Lie algebra ¶ ↺
    • depends_on proposition 15.7 Ideals of $A$ become ideals of $\mathfrak{g}_{A}$ ¶
      • depends_on definition 15.3 Tensor product Lie algebra ¶ ↺
      • depends_on theorem 15.4 The construction produces a Lie algebra ¶
        • depends_on definition 15.3 Tensor product Lie algebra ¶ ↺
        • proves proof ch:13-lie-algebra-expansions@proof-1 ¶
      • proves proof ch:13-lie-algebra-expansions@proof-3 ¶
    • proves proof ch:13-lie-algebra-expansions@proof-4 ¶
  • proves proof ch:13-lie-algebra-expansions@proof-9 ¶
• proves proof ch:13-lie-algebra-expansions@proof-11 ¶

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