Theorems · Theorem · nonassociative algebras
lie_skew
∀ {L : Type v} [inst : LieRing L] (x y : L), -⁅y, x⁆ = ⁅x, y⁆- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- LieRing
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.
Cited by26
Results whose statement or proof uses this declaration.
- LieAlgebra.IsKilling.finrank_rootSpace_eq_oneproof · cited by 6
- lie_mem_leftproof · cited by 6
- LieSubalgebra.mem_normalizer_iffproof · cited by 5
- LieAlgebra.Basis.iSup_cartan_borelLower_borelUpper_eq_topproof · cited by 4
- LieAlgebra.self_module_ker_eq_centerproof · cited by 3
- LieDerivation.ad_apply_applyproof · cited by 3
- IsSl2Triple.symmproof · cited by 2
- LieIdeal.idealizer_eq_normalizerproof · cited by 2
- LieModule.traceForm_apply_lie_apply'proof · cited by 2
- LieDerivation.apply_lie_eq_addproof · cited by 1
- LieSubmodule.lie_commproof · cited by 1
- lie_jacobiproof · cited by 1