Theorems · Theorem · nonassociative algebras
LieSubalgebra.ad_comp_incl_eq
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (K : LieSubalgebra R L)
(x : ↥K), (LieAlgebra.ad R L) ↑x ∘ₗ ↑K.incl = ↑K.incl ∘ₗ (LieAlgebra.ad R ↥K) x- Defined in
- Mathlib.Algebra.Lie.OfAssociative
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- LinearMap.compstatement · cited by 1,642
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LinearMap.extproof · cited by 844
- Module.Endstatement · cited by 774
- Bracket.bracketproof · cited by 642
- LieSubalgebrastatement and proof · cited by 418
- LieHomstatement · cited by 382
Cited by1
Results whose statement or proof uses this declaration.
- LieSubalgebra.isNilpotent_ad_of_isNilpotent_adproof · cited by 2