proposition 15.15 Takiff brackets

open in the book · parts/02-mathematical-methods/13-lie-algebra-expansions.tex:513 · p. 607

Rests on

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 ¶

Supports

depends_on example 15.16 The Maxwell tower ¶
depends_on proposition 15.26 The contraction along a grading ¶
- depends_on corollary 15.44 The eight vertices are the eight degenerations of $A$ ¶
  - depends_on remark 15.45 A correction this forces: the general splitting gives the static algebra, not Carroll ¶
- depends_on corollary 15.27 The flat limit ¶
  - depends_on corollary 15.36 Bargmann in $3{+}1$, extended Bargmann in $2{+}1$ ¶
    - depends_on example 15.64 The whole chapter at $D=4$ ¶
    - depends_on remark 15.59 The central charge is what makes the form work ¶
depends_on proposition 15.21 Resonance ¶

Neighborhood

Every logical edge within two steps of this node.

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partly declared
a check failed
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Edges

type	direction	node	provenance	where
`depends_on`	→	Truncated polynomial algebra and Takiff algebra	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:526
`depends_on`	→	Tensor product Lie algebra	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:526
`depends_on`	→	The radical of $A$ is solvable in $\mathfrak{g}_{A}$	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:526
`depends_on`	←	The Maxwell tower	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:557
`depends_on`	←	The contraction along a grading	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:794
`depends_on`	←	Resonance	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:643
`proves`	←	ch:13-lie-algebra-expansions@proof-9	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:529