example 15.16 The Maxwell tower
open in the book ·
parts/02-mathematical-methods/13-lie-algebra-expansions.tex:540
· p. 607
- example -- no derivation owed by its kind
Rests on
-
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 ¶
-
depends_on
definition 15.14
Truncated polynomial algebra and Takiff algebra
¶
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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 |