Theorems · Theorem · nonassociative algebras
lie_zero
∀ {L : Type v} {M : Type w} [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] (x : L),
⁅x, 0⁆ = 0- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 18 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 · cited by 642
- AddMonoidHom.map_zeroproof · cited by 47
- AddMonoidHom.mk'proof · cited by 25
- lie_addproof · cited by 19
Cited by20
Results whose statement or proof uses this declaration.
- LieModule.maxTrivSubmoduleproof · cited by 25
- LieSubmodule.lieIdeal_oper_eq_linear_spanproof · cited by 9
- lie_negproof · cited by 5
- IsSl2Triple.f_ne_zeroproof · cited by 3
- LieSubmodule.lie_baseChangeproof · cited by 3
- LieRingModule.toEndproof · cited by 3
- IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_fproof · cited by 3
- IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_ne_zero_of_eq_natproof · cited by 2
- LieModule.lie_mem_genWeightSpaceChain_of_genWeightSpace_eq_bot_rightproof · cited by 2
- IsSl2Triple.HasPrimitiveVectorWith.exists_natproof · cited by 2
- LieSubalgebra.isLieAbelian_lieSpan_iffproof · cited by 1
- LieSubalgebra.coe_lieSpan_eq_span_of_forall_lie_eq_zeroproof · cited by 1