Theorems · Theorem · nonassociative algebras

LieModule.genWeightSpace_genWeightSpaceOf_map_incl

∀ {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] (x : L) (χ : L → R),
  LieSubmodule.map (LieModule.genWeightSpaceOf M (χ x) x).incl
      (LieModule.genWeightSpace (↥(LieModule.genWeightSpaceOf M (χ x) x)) χ) =
    LieModule.genWeightSpace M χ

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

0 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent