Theorems · Theorem · nonassociative algebras

LieDerivation.ext_of_lieSpan_eq_top

∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} [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]
  {D1 D2 : LieDerivation R L M} (s : Set L), LieSubalgebra.lieSpan R L s = ⊤ → Set.EqOn (⇑D1) (⇑D2) s → D1 = D2

If the Lie span of a set is the whole Lie algebra, then two Lie derivations equal on this set are equal on the whole Lie algebra.

Defined in

Mathlib.Algebra.Lie.Derivation.Basic

Cited by

0 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule