Theorems · Theorem · nonassociative algebras
LieAlgebra.InvariantForm.orthogonal_toSubmodule
∀ {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),
↑(LieAlgebra.InvariantForm.orthogonal Φ hΦ_inv N) = Φ.orthogonal ↑N- Defined in
- Mathlib.Algebra.Lie.InvariantForm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LinearMap.BilinFormstatement and proof · cited by 501
- LieSubmodulestatement and proof · cited by 489
- LieSubmodule.toSubmodulestatement · cited by 150
- LinearMap.BilinForm.orthogonalstatement · cited by 36
- LinearMap.BilinForm.lieInvariantstatement and proof · cited by 14
- LieAlgebra.InvariantForm.orthogonalstatement · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.InvariantForm.orthogonal_isCompl_toSubmoduleproof · cited by 3