example 15.16 The Maxwell tower

open in the book · parts/02-mathematical-methods/13-lie-algebra-expansions.tex:540 · p. 607

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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 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 ¶

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type	direction	node	provenance	where
`cites`	→	Group-theoretical analysis of elementary particles in an external electromagnetic field	derived	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:552
`cites`	→	The Maxwell group and the quantum theory of particles in classical homogeneous electromagnetic fields	derived	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:552
`depends_on`	→	Takiff brackets	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:557