Theorems · Definition · nonassociative algebras
LieDerivation.toLinearMap
{R : Type u_1} →
{L : Type u_2} →
{M : Type u_3} →
[inst : CommRing R] →
[inst_1 : LieRing L] →
[inst_2 : LieAlgebra R L] →
[inst_3 : AddCommGroup M] →
[inst_4 : Module R M] →
[inst_5 : LieRingModule L M] → [inst_6 : LieModule R L M] → LieDerivation R L M → L →ₗ[R] MThe LinearMap underlying a LieDerivation.
- Defined in
- Mathlib.Algebra.Lie.Derivation.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
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.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieRingModulestatement and proof · cited by 727
- LieModulestatement and proof · cited by 424
- LieDerivationstatement and proof · cited by 95
Cited by18
Results whose statement or proof uses this declaration.
- LieDerivation.expstatement and proof · cited by 2
- LieDerivation.coe_ad_apply_eq_ad_applystatement · cited by 1
- Lie.Derivation.ofLieDerivationproof · cited by 1
- LieDerivation.toLinearMapLieHomproof · cited by 1
- LieDerivation.exp_applystatement and proof · cited by 1
- LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebraproof · cited by 1
- LieDerivation.leibniz'statement · cited by 1
- LieDerivation.coeFn_coestatement · cited by 0
- LieDerivation.coe_add_linearMapstatement · cited by 0
- LieDerivation.coe_neg_linearMapstatement · cited by 0
- LieDerivation.coe_smul_linearMapstatement · cited by 0
- Lie.Derivation.ofLieDerivation_applystatement · cited by 0