Theorems · Theorem · nonassociative algebras
LieAlgebra.lieCharacter_apply_lie
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
(χ : LieAlgebra.LieCharacter R L) (x y : L), χ ⁅x, y⁆ = 0- Defined in
- Mathlib.Algebra.Lie.Character
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- mul_commproof · cited by 2,262
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- sub_selfproof · cited by 996
- Bracket.bracketstatement · cited by 642
- LieRing.ofAssociativeRingstatement · cited by 227
- LieHom.map_lieproof · cited by 18
- LieAlgebra.LieCharacterstatement and proof · cited by 5
- LieRing.of_associative_ring_bracketproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.lieCharacter_apply_of_mem_derivedproof · cited by 0