Theorems · Theorem · nonassociative algebras
Function.Injective.isLieAbelian
∀ {R : Type u} {L₁ : Type v} {L₂ : Type w} [inst : CommRing R] [inst_1 : LieRing L₁] [inst_2 : LieRing L₂]
[inst_3 : LieAlgebra R L₁] [inst_4 : LieAlgebra R L₂] {f : L₁ →ₗ⁅R⁆ L₂},
Function.Injective ⇑f → IsLieAbelian L₂ → IsLieAbelian L₁- Defined in
- Mathlib.Algebra.Lie.Abelian
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- map_zeroproof · cited by 1,614
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketproof · cited by 642
- LieHomstatement and proof · cited by 382
- IsLieAbelianstatement and proof · cited by 55
- LieHom.map_lieproof · cited by 18
- trivial_lie_zeroproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.abelian_radical_iff_solvable_is_abelianproof · cited by 0
- lie_abelian_iff_equiv_lie_abelianproof · cited by 0