Theorems · Theorem · nonassociative algebras

LieModule.comap_genWeightSpace_eq_of_injective

∀ {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]
  [inst_7 : LieRing.IsNilpotent L] {M₂ : Type u_5} [inst_8 : AddCommGroup M₂] [inst_9 : Module R M₂]
  [inst_10 : LieRingModule L M₂] [inst_11 : LieModule R L M₂] {χ : L → R} {f : M →ₗ⁅R,L⁆ M₂},
  Function.Injective ⇑f → LieSubmodule.comap f (LieModule.genWeightSpace M₂ χ) = LieModule.genWeightSpace M χ

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

2 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotentAddCommGroupModuleLieRingModuleLieModule