Theorems · Theorem · nonassociative algebras

LieAlgebra.IsKilling.chainLength_of_eq_zsmul_add

∀ {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 β' : LieModule.Weight K (↥H) L)
  (n : ℤ), ⇑β' = n • ⇑α + ⇑β → LieAlgebra.IsKilling.chainLength α β' = LieAlgebra.IsKilling.chainLength α β

Defined in

Mathlib.Algebra.Lie.Weights.RootSystem

Cited by

0 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCharZeroLieRingLieAlgebraLieAlgebra.IsKillingFiniteDimensionalLieSubalgebra.IsCartanSubalgebraLieModule.IsTriangularizable