remark 15.59 The central charge is what makes the form work

Rests on

• depends_on corollary 15.36 Bargmann in $3{+}1$, extended Bargmann in $2{+}1$ ¶
  • depends_on corollary 15.35 Where the central charges are ¶
    • depends_on definition 15.24 The four kinematical gradings ¶
      • depends_on notation 15.22 Generators of $\mathfrak{so}(D-1,2)$ ¶
        • depends_on equation 14.90 eq:lie-algebrasopq ¶
    • depends_on theorem 15.34 The truncation tower is a tower of central extensions ¶
      • 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 14.72 Central extension ¶
      • depends_on proposition 15.6 Functoriality ¶
        • depends_on definition 15.3 Tensor product Lie algebra ¶
        • depends_on theorem 15.4 The construction produces a Lie algebra ¶
        • proves proof ch:13-lie-algebra-expansions@proof-2 ¶
      • depends_on proposition 14.73 The extension datum is a $2$-cocycle ¶
        • depends_on definition 14.72 Central extension ¶ ↺
        • proves proof ch:12-lie-groups-fibre-bundles@proof-35 ¶
      • proves proof ch:13-lie-algebra-expansions@proof-20 ¶
    • proves proof ch:13-lie-algebra-expansions@proof-21 ¶
  • depends_on corollary 15.27 The flat limit ¶
    • depends_on definition 15.24 The four kinematical gradings ¶ ↺
    • depends_on equation 14.99 eq:lie-poincare ¶
    • depends_on proposition 15.23 Brackets in the kinematical splitting ¶
      • depends_on equation 14.90 eq:lie-algebrasopq ¶ ↺
      • depends_on equation 14.128 eq:lie-kinematical-constants ¶
      • depends_on notation 15.22 Generators of $\mathfrak{so}(D-1,2)$ ¶ ↺
      • proves proof ch:13-lie-algebra-expansions@proof-12 ¶
    • depends_on proposition 15.26 The contraction along a grading ¶
      • depends_on definition 15.18 $\Z_{2}$-grading, symmetric coset ¶ ↺
      • depends_on definition 15.20 Resonant subalgebra ¶ ↺
      • depends_on equation 14.125 eq:lie-contraction ¶
      • 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 $\mathfrak{g}_{A}$ ¶
        • proves proof ch:13-lie-algebra-expansions@proof-9 ¶
      • proves proof ch:13-lie-algebra-expansions@proof-14 ¶
    • proves proof ch:13-lie-algebra-expansions@proof-15 ¶
  • depends_on proposition 25.14 The Galilei cocycle is not a coboundary ¶
    • depends_on definition 14.72 Central extension ¶ ↺
    • depends_on equation 25.15 eq:pq-galilei-central ¶
    • depends_on proposition 14.73 The extension datum is a $2$-cocycle ¶ ↺
    • proves proof ch:08-poisson-quantum-bridge@proof-7 ¶
  • depends_on theorem 15.34 The truncation tower is a tower of central extensions ¶ ↺
  • proves proof ch:13-lie-algebra-expansions@proof-22 ¶
• depends_on theorem 15.58 Nondegeneracy on a resonant subalgebra ¶
  • depends_on definition 15.20 Resonant subalgebra ¶ ↺
  • depends_on lemma 15.19 A grading is an involution, and the Killing form respects it ¶
    • depends_on definition 15.18 $\Z_{2}$-grading, symmetric coset ¶ ↺
    • proves proof ch:13-lie-algebra-expansions@proof-10 ¶
  • 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 ¶
  • proves proof ch:13-lie-algebra-expansions@proof-33 ¶

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