Theorems · Theorem · nonassociative algebras

LieModule.LinearWeights.map_smul

∀ {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} [self : LieModule.LinearWeights R L M] (χ : L → R),
  LieModule.genWeightSpace M χ ≠ ⊥ → ∀ (t : R) (x : L), χ (t • x) = t • χ x

Defined in

Mathlib.Algebra.Lie.Weights.Linear

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LieModule.LinearWeights