Theorems · Definition · nonassociative algebras

LieAlgebra.InvariantForm.orthogonal

{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] →
              [inst_4 : LieRingModule L M] →
                (Φ : LinearMap.BilinForm R M) →
                  LinearMap.BilinForm.lieInvariant L Φ → LieSubmodule R L M → LieSubmodule R L M

The orthogonal complement of a Lie submodule N with respect to an invariant bilinear form Φ is the Lie submodule of elements y such that Φ x y = 0 for all x ∈ N.

Defined in

Mathlib.Algebra.Lie.InvariantForm

Cited by

10 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule