Theorems · Theorem · nonassociative algebras

LieAlgebra.IsKilling.lieIdealOrderIso_left_inv

∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : CharZero K] [inst_2 : LieRing L] [inst_3 : LieAlgebra K L]
  [inst_4 : FiniteDimensional K L] [inst_5 : LieAlgebra.IsKilling K L] {H : LieSubalgebra K L}
  [inst_6 : H.IsCartanSubalgebra] [inst_7 : LieModule.IsTriangularizable K (↥H) L] (I : LieIdeal K L)
  (hI :
    optParam
      (∀ (α : ↥LieSubalgebra.root),
        I.rootSpan ∈ Module.End.invtSubmodule ↑((LieAlgebra.IsKilling.rootSystem H).reflection α))
      ⋯),
  LieAlgebra.IsKilling.invtSubmoduleToLieIdeal I.rootSpan hI = I

Defined in

Mathlib.Algebra.Lie.Weights.IsSimple

Cited by

0 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCharZeroLieRingLieAlgebraFiniteDimensionalLieAlgebra.IsKillingLieSubalgebra.IsCartanSubalgebraLieModule.IsTriangularizable