Theorems · Theorem · nonassociative algebras

LieIdeal.restr_eq_iSup_sl2SubmoduleOfRoot

∀ {K : Type u_1} {L : Type u_2} [inst : Field K] [inst_1 : LieRing L] [inst_2 : LieAlgebra K L]
  [inst_3 : FiniteDimensional K L] {H : LieSubalgebra K L} [inst_4 : H.IsCartanSubalgebra] [inst_5 : CharZero K]
  [inst_6 : LieAlgebra.IsKilling K L] [inst_7 : LieModule.IsTriangularizable K (↥H) L] (I : LieIdeal K L),
  LieSubmodule.restr I H = ⨆ α ∈ I.rootSet, LieAlgebra.IsKilling.sl2SubmoduleOfRoot ⋯

Defined in

Mathlib.Algebra.Lie.Weights.IsSimple

Cited by

1 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLieRingLieAlgebraFiniteDimensionalLieSubalgebra.IsCartanSubalgebraCharZeroLieAlgebra.IsKillingLieModule.IsTriangularizable