Theorems · Theorem · nonassociative algebras

LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt

∀ {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 : LieAlgebra.IsKilling K L] [inst_5 : FiniteDimensional K L] {H : LieSubalgebra K L}
  [inst_6 : H.IsCartanSubalgebra] [inst_7 : LieModule.IsTriangularizable K (↥H) L] (α β : LieModule.Weight K (↥H) L),
  α.IsNonZero →
    ∀ {n : ℕ},
      LieAlgebra.IsKilling.chainLength α β < n → LieAlgebra.rootSpace H (-(n • ⇑α) + ⇑(LieModule.chainTop (⇑α) β)) = ⊥

Defined in

Mathlib.Algebra.Lie.Weights.RootSystem

Cited by

3 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCharZeroLieRingLieAlgebraLieAlgebra.IsKillingFiniteDimensionalLieSubalgebra.IsCartanSubalgebraLieModule.IsTriangularizable