definition 15.9 Trace form of an algebra

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Supports

• depends_on proposition 15.42 The $\Gamma$-graded commutative algebras ¶
  • depends_on corollary 15.46 The sign data, hypothesis (H3), and the count eleven ¶
  • depends_on theorem 15.43 The three constants of the classification are the three structure constants of $A$ ¶
    • depends_on corollary 15.46 The sign data, hypothesis (H3), and the count eleven ¶ ↺
    • 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 proposition 15.28 The quadratic family ¶
  • depends_on corollary 15.32 The expansion parameter is the cosmological constant ¶
    • depends_on example 15.64 The whole chapter at $D=4$ ¶
    • depends_on remark 15.63 The inclusion is strict, and the strictness is physical ¶
    • depends_on remark 15.33 Which branch nature is on ¶
  • depends_on remark 15.63 The inclusion is strict, and the strictness is physical ¶ ↺
  • depends_on theorem 15.29 The three constant-curvature kinematics, in every dimension ¶
    • depends_on corollary 15.32 The expansion parameter is the cosmological constant ¶ ↺
    • depends_on example 15.64 The whole chapter at $D=4$ ¶ ↺
• depends_on theorem 15.10 Factorisation of the Killing form ¶
  • depends_on corollary 15.11 Semisimplicity criterion ¶
    • depends_on proposition 15.42 The $\Gamma$-graded commutative algebras ¶ ↺
    • depends_on proposition 15.28 The quadratic family ¶ ↺
    • depends_on theorem 15.13 Classification of $\mathfrak{g}_{A}$ by the algebra ¶
  • depends_on example 15.57 $k=2$ recovers the Killing form ¶
    • depends_on proposition 15.55 Completeness fails for $k\ge3$ ¶