definition 15.18 $\Z_{2}$-grading, symmetric coset

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Supports

• depends_on definition 15.20 Resonant subalgebra ¶
  • depends_on example 15.61 Maurer–Cartan expansion ¶
  • 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 ¶
  • depends_on theorem 15.58 Nondegeneracy on a resonant subalgebra ¶
    • depends_on corollary 15.69 No positive pairing survives the radical ¶
    • depends_on remark 15.59 The central charge is what makes the form work ¶ ↺
  • depends_on theorem 15.34 The truncation tower is a tower of central extensions ¶
    • 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 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 lemma 15.19 A grading is an involution, and the Killing form respects it ¶
  • depends_on lemma 15.40 The three symmetric cosets are one $\Z_{2}\times\Z_{2}$-grading ¶
    • 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 theorem 15.43 The three constants of the classification are the three structure constants of $A$ ¶ ↺
  • depends_on theorem 15.58 Nondegeneracy on a resonant subalgebra ¶ ↺
• depends_on proposition 15.26 The contraction along a grading ¶ ↺
• depends_on proposition 15.21 Resonance ¶ ↺
• depends_on proposition 15.25 Which of the four are symmetric cosets ¶
  • depends_on lemma 15.40 The three symmetric cosets are one $\Z_{2}\times\Z_{2}$-grading ¶ ↺
• depends_on theorem 15.34 The truncation tower is a tower of central extensions ¶ ↺