equation 14.90 eq:lie-algebrasopq

Rests on

No declared or derived dependency edges point away from this node yet.

Supports

• depends_on corollary A.344 The algebras $\mathfrak{so}(p,q)$ are semisimple ¶
  • depends_on corollary A.411 Semisimple algebras admit no nontrivial extension ¶
  • depends_on example A.359 The Lorentz algebra ¶
• depends_on lemma 14.64 Properties of $W$ ¶
  • depends_on theorem 14.65 The two Casimir operators of the Poincaré algebra in $3+1$ dimensions ¶
    • depends_on example A.394 $D = 4$ ¶
• depends_on notation 15.22 Generators of $\mathfrak{so}(D-1,2)$ ¶
  • depends_on definition 15.24 The four kinematical gradings ¶
    • 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 remark 15.59 The central charge is what makes the form work ¶
      • depends_on example 15.64 The whole chapter at $D=4$ ¶ ↺
    • 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 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 theorem 15.43 The three constants of the classification are the three structure constants of $A$ ¶ ↺
    • 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 15.29 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 remark 15.63 The inclusion is strict, and the strictness is physical ¶
        • depends_on remark 15.33 Which branch nature is on ¶
      • depends_on example 15.64 The whole chapter at $D=4$ ¶ ↺
  • depends_on proposition 15.23 Brackets in the kinematical splitting ¶
    • depends_on corollary 15.46 The sign data, hypothesis (H3), and the count eleven ¶ ↺
    • depends_on corollary 15.27 The flat limit ¶ ↺
    • depends_on lemma 15.40 The three symmetric cosets are one $\Z_{2}\times\Z_{2}$-grading ¶ ↺
    • depends_on proposition 15.25 Which of the four are symmetric cosets ¶ ↺
    • depends_on theorem 15.29 The three constant-curvature kinematics, in every dimension ¶ ↺
• depends_on proposition 15.23 Brackets in the kinematical splitting ¶ ↺
• depends_on proposition 14.70 The conformal algebra of flat space ¶
• depends_on proposition 14.22 The rank of $\mathfrak{so}(p,q)$ ¶
  • depends_on lemma 14.68 The algebra fixing a timelike momentum ¶
    • depends_on definition A.384 The mass shell and the standard momentum ¶
      • depends_on lemma A.387 Standard boost and transitivity ¶
        • depends_on lemma A.388 The invariant measure ¶
        • depends_on proposition A.390 Construction ¶
      • depends_on lemma A.386 The little group ¶
        • depends_on proposition A.390 Construction ¶ ↺
      • depends_on lemma A.388 The invariant measure ¶ ↺
      • depends_on theorem A.385 Labels of a massive representation ¶
        • depends_on example A.394 $D = 4$ ¶ ↺
      • depends_on theorem A.392 Wigner–Mackey classification; quoted ¶
    • depends_on lemma A.386 The little group ¶ ↺
    • depends_on theorem A.385 Labels of a massive representation ¶ ↺