Treatise of Physics

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lemma A.350 Invariant polynomials on $\mathfrak{g}$

open in the book · appendices/A-long-proofs.tex:17041 · p. 2961

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lemma A.350: Invariant polynomials on gA.350definition 14.14: Invariant symmetric tensor14.14definition 14.10: Killing form14.10theorem A.330: Cartan's criterion for semisimplicityA.330theorem A.351: Chevalley restriction theorem, quotedA.351proof : app:A-long-proofs@proof-216proofequation 14.5: eq:lie-structconst14.5theorem 14.16: Invariant tensors give Casimir operators14.16corollary A.343: The Killing form of a simple idealA.343corollary 14.12: Total antisymmetry of the structure constants14.12definition A.424: Loop algebra and residueA.424definition A.400: Invariant form, dual basis, CasimirA.400lemma 14.11: Invariance of the Killing form14.11proposition A.334: Nondegeneracy implies no abelian idealA.334proposition 14.84: Properties of a contraction14.84theorem 14.13: Cartan's criterion14.13corollary A.344: The algebras so(p,q) are semisimpleA.344corollary A.342: Orthogonal splitting of idealsA.342lemma A.402: The trace form is nondegenerate for a faithful representationA.402theorem A.346: RacahA.346proof : app:A-long-proofs@proof-209proofdefinition 14.20: Cartan subalgebra and rank14.20

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typedirectionnode provenancewhere
depends_on → Invariant symmetric tensor declared appendices/A-long-proofs.tex:17056
depends_on → Killing form declared appendices/A-long-proofs.tex:17056
depends_on → Cartan's criterion for semisimplicity declared appendices/A-long-proofs.tex:17056
depends_on ← Chevalley restriction theorem, quoted declared appendices/A-long-proofs.tex:17096
proves ← app:A-long-proofs@proof-216 declared appendices/A-long-proofs.tex:17059