Theorems · Definition · nonassociative algebras
LieIdeal.toLieSubalgebra
(R : Type u) →
(L : Type v) →
[inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → LieIdeal R L → LieSubalgebra R LAn ideal of a Lie algebra is a Lie subalgebra.
- Defined in
- Mathlib.Algebra.Lie.Ideal
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Submoduleproof · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieSubalgebrastatement · cited by 418
- LieIdealstatement and proof · cited by 282
- LieSubmodule.toSubmoduleproof · cited by 150
Cited by55
Results whose statement or proof uses this declaration.
- LieIdeal.mapproof · cited by 33
- LieIdeal.comapproof · cited by 21
- LieIdeal.inclproof · cited by 17
- LieHom.IsIdealMorphismproof · cited by 10
- LieAlgebra.IsKilling.ker_killingForm_eq_botproof · cited by 7
- LieIdeal.toLieSubalgebra_toSubmodulestatement · cited by 5
- LieAlgebra.IsKilling.root_apply_cartanEquivDual_symm_ne_zeroproof · cited by 4
- LieHom.isIdealMorphism_defstatement · cited by 4
- LieIdeal.coe_bracket_of_moduleproof · cited by 4
- LieSubmodule.lie_abelian_iff_lie_self_eq_botproof · cited by 3
- LieIdeal.incl_coestatement · cited by 2
- LieIdeal.incl_rangestatement and proof · cited by 2