Theorems · Theorem · nonassociative algebras

LieAlgebra.lieIdeal_eq_inf_cartan_sup_biSup_inf_rootSpace

∀ {L : Type u_2} [inst : LieRing L] {K : Type u_4} [inst_1 : Field K] [inst_2 : LieAlgebra K L] [FiniteDimensional K L]
  (H : LieSubalgebra K L) [inst_4 : H.IsCartanSubalgebra] [LieModule.IsTriangularizable K (↥H) L] (I : LieIdeal K L),
  LieSubmodule.restr I H =
    LieSubmodule.restr I H ⊓ H.toLieSubmodule ⊔
      ⨆ α, ⨆ (_ : α.IsNonZero), LieSubmodule.restr I H ⊓ LieAlgebra.rootSpace H ⇑α

Defined in

Mathlib.Algebra.Lie.Weights.Cartan

Cited by

1 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingFieldLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebraLieModule.IsTriangularizable