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Expansions of Lie Algebras
Expansions of Lie Algebras
foundations results +27 more equations depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) step_from (declared) step_from (declared) notation 15.1: Standing conventions of this chapter 15.1 Standing convent… definition 15.3: Tensor product Lie algebra 15.3 Tensor product L… definition 15.9: Trace form of an algebra 15.9 Trace form of an… definition 15.14: Truncated polynomial algebra and Takiff algebra 15.14 Truncated polyno… definition 15.18: ℤ_2-grading, symmetric coset 15.18 ℤ_2-grading, sym… definition 15.20: Resonant subalgebra 15.20 Resonant subalge… notation 15.22: Generators of so(D-1,2) 15.22 Generators of so… definition 15.24: The four kinematical gradings 15.24 The four kinemat… definition 15.49: k-trace 15.49 k-trace definition 15.52: Balanced form 15.52 Balanced form definition 15.66: Gram form of a functional 15.66 Gram form of a f… theorem 15.4: The construction produces a Lie algebra 15.4 The construction… proposition 15.6: Functoriality 15.6 Functoriality proposition 15.7: Ideals of A become ideals of g_A 15.7 Ideals of A beco… proposition 15.8: The radical of A is solvable in g_A 15.8 The radical of A… theorem 15.10: Factorisation of the Killing form 15.10 Factorisation of… corollary 15.11: Semisimplicity criterion 15.11 Semisimplicity c… lemma 15.12: Artin decomposition 15.12 Artin decomposit… theorem 15.13: Classification of g_A by the algebra 15.13 Classification o… proposition 15.15: Takiff brackets 15.15 Takiff brackets lemma 15.19: A grading is an involution, and the Killing form respects it 15.19 A grading is an… proposition 15.21: Resonance 15.21 Resonance proposition 15.23: Brackets in the kinematical splitting 15.23 Brackets in the… proposition 15.25: Which of the four are symmetric cosets 15.25 Which of the fou… equation 15.2: eq:exp-bracket eq. (15.2) equation 15.33: eq:exp-einstein eq. (15.33) equation 15.37: eq:exp-ricci-lambda eq. (15.37) equation 15.61: eq:exp-factorised-form eq. (15.61) equation 15.69: eq:exp-pairing eq. (15.69) The chain of Expansions of Lie Algebras: 29 of 56 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.