definition 15.24 The four kinematical gradings

open in the book · parts/02-mathematical-methods/13-lie-algebra-expansions.tex:727 · p. 609

ground object -- no derivation owed

Rests on

depends_on notation 15.22 Generators of $\mathfrak{so}(D-1,2)$ ¶
- depends_on equation 14.90 eq:lie-algebrasopq ¶

Supports

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 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 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 $D=4$ ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Generators of $\mathfrak{so}(D-1,2)$	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:741
`depends_on`	←	Where the central charges are	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:1235
`depends_on`	←	The eight vertices are the eight degenerations of $A$	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:1713
`depends_on`	←	The flat limit	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:836
`depends_on`	←	The three symmetric cosets are one $\Z_{2}\times\Z_{2}$-grading	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:1487
`depends_on`	←	Which of the four are symmetric cosets	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:748
`depends_on`	←	The three constant-curvature kinematics, in every dimension	declared	parts/02-mathematical-methods/13-lie-algebra-expansions.tex:920