Theorems · Theorem · nonassociative algebras

Equiv.lieModule_isNilpotent_iff

∀ {R : Type u} {L : Type v} {M : Type w} [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] [LieModule R L M] {L₂ : Type u_1}
  {M₂ : Type u_2} [inst_7 : LieRing L₂] [inst_8 : LieAlgebra R L₂] [inst_9 : AddCommGroup M₂] [inst_10 : Module R M₂]
  [inst_11 : LieRingModule L₂ M₂] [LieModule R L₂ M₂] (f : L ≃ₗ⁅R⁆ L₂) (g : M ≃ₗ[R] M₂),
  (∀ (x : L) (m : M), ⁅f x, g m⁆ = g ⁅x, m⁆) → (LieModule.IsNilpotent L M ↔ LieModule.IsNilpotent L₂ M₂)

Defined in

Mathlib.Algebra.Lie.Nilpotent

Cited by

2 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule