Theorems · Theorem · nonassociative algebras
lie_lie
∀ {L : Type v} {M : Type w} [inst : LieRing L] [inst_1 : AddCommGroup M] [inst_2 : LieRingModule L M] (x y : L) (m : M),
⁅⁅x, y⁆, m⁆ = ⁅x, ⁅y, m⁆⁆ - ⁅y, ⁅x, m⁆⁆- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- add_sub_cancel_rightproof · cited by 187
- leibniz_lieproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- LieModule.toEnd_lieproof · cited by 2
- lie_jacobiproof · cited by 1
- LieSubalgebra.isLieAbelian_lieSpan_iffproof · cited by 1
- LieModule.trace_toEnd_genWeightSpaceChain_eq_zeroproof · cited by 1
- IsSl2Triple.HasPrimitiveVectorWith.mk'proof · cited by 0
- FreeLieAlgebra.liftAux_specproof · cited by 0
- LieModule.Cohomology.d₂₃_comp_d₁₂proof · cited by 0
- cross_crossproof · cited by 0