Theorems · Theorem · nonassociative algebras
LieSubalgebra.isNilpotent_ad_of_isNilpotent_ad
∀ {R : Type u_1} [inst : CommRing R] {L : Type u_3} [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
(K : LieSubalgebra R L) {x : ↥K}, IsNilpotent ((LieAlgebra.ad R L) ↑x) → IsNilpotent ((LieAlgebra.ad R ↥K) x)- Defined in
- Mathlib.Algebra.Lie.AdjointAction.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
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 and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Module.Endstatement · cited by 774
- LieSubalgebrastatement and proof · cited by 418
- LieHomstatement · cited by 382
- IsNilpotentstatement and proof · cited by 248
- LieRing.ofAssociativeRingstatement · cited by 227
- LieAlgebra.adstatement and proof · cited by 49
- Module.End.submodule_pow_eq_zero_of_pow_eq_zeroproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- LieIdeal.isSolvable_of_killingForm_apply_lie_eq_zeroproof · cited by 2
- LieAlgebra.isNilpotent_ad_of_isNilpotentproof · cited by 1