Theorems · Theorem · nonassociative algebras

LieAlgebra.InvariantForm.mem_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)
  (hΦ_inv : LinearMap.BilinForm.lieInvariant L Φ) (N : LieSubmodule R L M) (y : M),
  y ∈ LieAlgebra.InvariantForm.orthogonal Φ hΦ_inv N ↔ ∀ x ∈ N, (Φ x) y = 0

Defined in

Mathlib.Algebra.Lie.InvariantForm

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule