Theorems · Definition · nonassociative algebras
LieHom.range
{R : Type u} →
{L : Type v} →
[inst : CommRing R] →
[inst_1 : LieRing L] →
[inst_2 : LieAlgebra R L] →
{L₂ : Type w} → [inst_3 : LieRing L₂] → [inst_4 : LieAlgebra R L₂] → (L →ₗ⁅R⁆ L₂) → LieSubalgebra R L₂The range of a morphism of Lie algebras is a Lie subalgebra.
- Defined in
- Mathlib.Algebra.Lie.Subalgebra
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LinearMap.rangeproof · cited by 893
- LieSubalgebrastatement · cited by 418
- LieHomstatement and proof · cited by 382
- LieHom.toLinearMapproof · cited by 74
Cited by55
Results whose statement or proof uses this declaration.
- LieHom.idealRangeproof · cited by 17
- LieHom.IsIdealMorphismproof · cited by 10
- LieSubalgebra.ofLeproof · cited by 8
- LieHom.mem_range_selfstatement · cited by 5
- LieHom.isIdealMorphism_defstatement · cited by 4
- LieHom.range_eq_topstatement and proof · cited by 4
- LieIdeal.incl_idealRangeproof · cited by 3
- LieHom.quotKerEquivRangestatement · cited by 3
- LieHom.rangeRestrictstatement · cited by 3
- LieHom.range_toSubmodulestatement · cited by 3
- LieIdeal.incl_isIdealMorphismproof · cited by 2
- LieIdeal.incl_rangestatement · cited by 2