Theorems · Theorem · nonassociative algebras
LieAlgebra.ad_eq_lmul_left_sub_lmul_right
∀ {R : Type u} [inst : CommRing R] (A : Type v) [inst_1 : Ring A] [inst_2 : Algebra R A],
⇑(LieAlgebra.ad R A) = LinearMap.mulLeft R - LinearMap.mulRight R- Defined in
- Mathlib.Algebra.Lie.OfAssociative
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- LinearMap.extproof · cited by 844
- Module.Endstatement · cited by 774
- LieHomstatement · cited by 382
- LieRing.ofAssociativeRingstatement · cited by 227
- LieAlgebra.adstatement · cited by 49
- LinearMap.mulLeftstatement · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- LieAlgebra.ad_nilpotent_of_nilpotentproof · cited by 2
- JacobsonNoether.exist_pow_eq_zero_of_leproof · cited by 1
- LieAlgebra.ad_isSemisimple_of_isSemisimpleproof · cited by 1