Theorems · Theorem · nonassociative algebras

LieModule.lie_mem_maxGenEigenspace_toEnd

∀ {R : Type u_2} {L : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M] {χ₁ χ₂ : R}
  {x y : L} {m : M},
  y ∈ ((LieModule.toEnd R L L) x).maxGenEigenspace χ₁ →
    m ∈ ((LieModule.toEnd R L M) x).maxGenEigenspace χ₂ →
      ⁅y, m⁆ ∈ ((LieModule.toEnd R L M) x).maxGenEigenspace (χ₁ + χ₂)

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule