Theorems · Definition · nonassociative algebras
LieAlgebra.derivedSeries
(R : Type u) → (L : Type v) → [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → ℕ → LieIdeal R L
The derived series of Lie ideals of a Lie algebra.
- Defined in
- Mathlib.Algebra.Lie.Solvable
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Top.topproof · cited by 9,680
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieIdealstatement · cited by 282
- LieAlgebra.derivedSeriesOfIdealproof · cited by 28
Cited by31
Results whose statement or proof uses this declaration.
- LieAlgebra.derivedSeries_defstatement · cited by 5
- LieAlgebra.isSolvable_iffstatement and proof · cited by 5
- LieIdeal.derivedSeries_eq_bot_iffstatement and proof · cited by 4
- LieAlgebra.IsSolvable.solvablestatement · cited by 3
- LieIdeal.isSolvable_of_killingForm_apply_lie_eq_zeroproof · cited by 2
- LieAlgebra.derivedSeries_baseChangestatement and proof · cited by 2
- Function.Injective.lieAlgebra_isSolvableproof · cited by 2
- LieIdeal.derivedSeries_eq_derivedSeriesOfIdeal_comapstatement and proof · cited by 2
- LieAlgebra.coe_derivedSeries_one_eqstatement · cited by 1
- LieAlgebra.IsSolvable.casesOnstatement and proof · cited by 1
- LieAlgebra.IsSolvable.mkstatement and proof · cited by 1
- LieModule.isNilpotent_derivedSeries_of_traceForm_eq_zerostatement and proof · cited by 1