Theorems · Definition · nonassociative algebras
LieDerivation.IsKilling.rangeAdOrthogonal
(R : Type u_1) →
(L : Type u_2) →
[inst : Field R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → LieSubmodule R L (LieDerivation R L L)The orthogonal complement of the inner derivations is a Lie submodule of all derivations.
- Defined in
- Mathlib.Algebra.Lie.Derivation.Killing
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Submoduleproof · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieSubmodulestatement · cited by 489
- LieDerivationstatement and proof · cited by 95
- LieSubalgebra.toSubmoduleproof · cited by 90
- LieHom.rangeproof · cited by 44
- LinearMap.BilinForm.orthogonalproof · cited by 36
- killingFormproof · cited by 34
- LieDerivation.adproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- LieDerivation.IsKilling.ad_mem_orthogonal_of_mem_orthogonalproof · cited by 1
- LieDerivation.IsKilling.rangeAdOrthogonal_carrierstatement · cited by 0