Theorems · Theorem · nonassociative algebras
LieHom.map_lie
∀ {R : Type u} {L₁ : Type v} {L₂ : Type w} [inst : CommRing R] [inst_1 : LieRing L₁] [inst_2 : LieAlgebra R L₁]
[inst_3 : LieRing L₂] [inst_4 : LieAlgebra R L₂] (f : L₁ →ₗ⁅R⁆ L₂) (x y : L₁), f ⁅x, y⁆ = ⁅f x, f y⁆- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
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.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketstatement · cited by 642
- LieHomstatement and proof · cited by 382
- LieHom.map_lie'proof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- LieModule.traceForm_apply_lie_applyproof · cited by 5
- LieIdeal.map_bracket_leproof · cited by 4
- Function.Injective.isLieAbelianproof · cited by 2
- LieHom.toNonUnitalAlgHomproof · cited by 2
- LieIdeal.map_bracket_eqproof · cited by 2
- LieIdeal.coe_map_of_surjectiveproof · cited by 2
- LieIdeal.comap_bracket_eqproof · cited by 2
- LieEquiv.map_lieproof · cited by 2
- LieAlgebra.Extension.ringModuleOf_bracket_projproof · cited by 1
- LieAlgebra.commute_ad_of_commuteproof · cited by 1
- LieAlgebra.IsKilling.eq_zero_of_isNilpotent_ad_of_mem_isCartanSubalgebraproof · cited by 1
- LieAlgebra.lieCharacter_apply_lieproof · cited by 1