Theorems · Definition · nonassociative algebras

LinearMap.BilinForm.lieInvariant

{R : Type u_1} →
  (L : Type u_2) →
    {M : Type u_3} →
      [inst : CommRing R] →
        [inst_1 : LieRing L] →
          [inst_2 : AddCommGroup M] → [inst_3 : Module R M] → [LieRingModule L M] → LinearMap.BilinForm R M → Prop

A bilinear form on a Lie module M of a Lie algebra L is invariant if for all x : L and y z : M the condition Φ ⁅x, y⁆ z = -Φ y ⁅x, z⁆ holds.

Defined in

Mathlib.Algebra.Lie.InvariantForm

Cited by

14 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule