Theorems · Definition · nonassociative algebras
LieIdeal.killingCompl
(R : Type u_1) → (L : Type u_3) → [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → LieIdeal R L → LieIdeal R L
The orthogonal complement of an ideal with respect to the killing form is an ideal.
- Defined in
- Mathlib.Algebra.Lie.TraceForm
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieIdealstatement and proof · cited by 282
- killingFormproof · cited by 34
- LieAlgebra.InvariantForm.orthogonalproof · cited by 10
Cited by10
Results whose statement or proof uses this declaration.
- LieIdeal.mem_killingComplstatement · cited by 2
- LieAlgebra.IsKilling.killingCompl_top_eq_botstatement · cited by 2
- LieIdeal.toSubmodule_killingComplstatement · cited by 1
- LieAlgebra.isKilling_of_equivproof · cited by 1
- LieIdeal.le_killingCompl_top_of_isLieAbelianstatement · cited by 1
- LieAlgebra.killingCompl_top_le_radicalstatement and proof · cited by 0
- LieIdeal.coe_killingCompl_topstatement · cited by 0
- LieIdeal.isCompl_killingComplstatement and proof · cited by 0
- LieAlgebra.IsKilling.casesOnstatement and proof · cited by 0
- LieAlgebra.IsKilling.recOnstatement and proof · cited by 0