Lie

Results named in Tau Ceti's TauCeti.Algebra.Lie modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

Abstract Jordan decomposition… to The Racah–Speiser formula, in…

• Abstract Jordan decomposition, existence
• The Brauer–Klimyk formula, in group-algebra form
• Cartan's formula ι_x d ω = L_x ω - d ι_x ω
• Chevalley's rank-one identity
• The Chevalley–Eilenberg formula for the differential of a cochain of positive degree
• The first isomorphism theorem for a surjective homomorphism of Lie algebras
• Freudenthal's multiplicity formula
• The Frobenius commutator identity
• The Jacobi identity, for a positive definite B with even diagonal
• Jacobson's lemma for the adjoint representation
• Jordan–Chevalley decomposition of a derivation
• Kostant's multiplicity formula
• The lattice form of Weyl's theorem
• The Leibniz form of the Jacobi identity, for a positive definite B with even diagonal
• The Levi decomposition
• Levi's theorem
• The linear-independence half of the Poincaré--Birkhoff--Witt theorem
• The Poincaré--Birkhoff--Witt theorem
• The positive-simple-root Chevalley collection formula over 𝔽₃
• The Racah–Speiser formula, in group-algebra form

Schur's lemma for Lie modules to Weyl's theorem as a…

• Schur's lemma for Lie modules
• The structure theorem for reductive Lie algebras
• The Weyl character formula
• The Weyl dimension formula (TauCeti.finrank_eq_prod_coweightPairing_div)
• Weyl's complete reducibility theorem
• Weyl's theorem as a decomposition

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