Theorems · Theorem · nonassociative algebras
zero_lie
∀ {L : Type v} {M : Type w} [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] (m : M),
⁅0, m⁆ = 0- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 15 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.
- AddCommGroupstatement and proof · cited by 12,871
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- Bracket.bracketstatement and proof · cited by 642
- AddMonoidHom.map_zeroproof · cited by 47
- AddMonoidHom.mk'proof · cited by 25
- add_lieproof · cited by 20
Cited by16
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZeroproof · cited by 5
- IsSl2Triple.e_ne_zeroproof · cited by 4
- neg_lieproof · cited by 4
- LieSubmodule.lie_baseChangeproof · cited by 3
- LieAlgebra.Basis.baseSupp_apply_smul_eproof · cited by 3
- LieAlgebra.IsKilling.corootSpace_zero_eq_botproof · cited by 2
- LieModule.isFaithful_iff_ker_eq_botproof · cited by 2
- LieSubalgebra.isLieAbelian_lieSpan_iffproof · cited by 1
- LieSubalgebra.coe_lieSpan_eq_span_of_forall_lie_eq_zeroproof · cited by 1
- nsmul_lieproof · cited by 1
- LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebraproof · cited by 1
- DirectSum.lie_of_of_neproof · cited by 1