Theorems · Theorem · nonassociative algebras

LieDerivation.mem_ad_idealRange_iff

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  {D : LieDerivation R L L}, D ∈ (LieDerivation.ad R L).idealRange ↔ ∃ x, (LieDerivation.ad R L) x = D

A derivation D belongs to the ideal range of the adjoint action iff it is of the form ad x for some x in the Lie algebra L.

Defined in

Mathlib.Algebra.Lie.AdjointAction.Derivation

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra