Theorems · Theorem · nonassociative algebras

LieModule.traceForm_apply_lie_apply

∀ (R : Type u_1) (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] (x y z : L),
  ((LieModule.traceForm R L M) ⁅x, y⁆) z = ((LieModule.traceForm R L M) x) ⁅y, z⁆

The trace form of a Lie module is compatible with the action of the Lie algebra. See also LieModule.traceForm_apply_lie_apply'.

Defined in

Mathlib.Algebra.Lie.TraceForm

Cited by

5 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule