Theorems · Theorem · nonassociative algebras

LieModule.isNilpotent_toEnd_of_mem_rootSpace

∀ {L : Type u_2} [inst : LieRing L] (M : Type u_3) [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] {K : Type u_4}
  [inst_3 : Field K] [CharZero K] [inst_5 : LieAlgebra K L] (H : LieSubalgebra K L) [inst_6 : LieRing.IsNilpotent ↥H]
  [inst_7 : Module K M] [inst_8 : LieModule K L M] [LieModule.IsTriangularizable K (↥H) M] [FiniteDimensional K M]
  {x : L} {χ : ↥H → K}, χ ≠ 0 → x ∈ LieAlgebra.rootSpace H χ → IsNilpotent ((LieModule.toEnd K L M) x)

Defined in

Mathlib.Algebra.Lie.Weights.Chain

Cited by

1 results in Mathlib

Foundations

Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieRingAddCommGroupLieRingModuleFieldCharZeroLieAlgebraLieRing.IsNilpotentModuleLieModuleLieModule.IsTriangularizableFiniteDimensional