Theorems · Theorem · nonassociative algebras
LieAlgebra.derivedSeriesOfIdeal_succ
∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L)
(k : ℕ),
LieAlgebra.derivedSeriesOfIdeal R L (k + 1) I =
⁅LieAlgebra.derivedSeriesOfIdeal R L k I, LieAlgebra.derivedSeriesOfIdeal R L k I⁆- Defined in
- Mathlib.Algebra.Lie.Solvable
- Cited by
- 14 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.
Cites7
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
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Bracket.bracketstatement and proof · cited by 642
- LieIdealstatement and proof · cited by 282
- Function.iterate_succ_apply'proof · cited by 72
- LieAlgebra.derivedSeriesOfIdealstatement · cited by 28
Cited by14
Results whose statement or proof uses this declaration.
- LieAlgebra.derivedSeriesOfIdeal_leproof · cited by 4
- LieIdeal.isSolvable_of_killingForm_apply_lie_eq_zeroproof · cited by 2
- LieAlgebra.derivedSeriesOfIdeal_addproof · cited by 2
- LieIdeal.derivedSeries_eq_derivedSeriesOfIdeal_comapproof · cited by 2
- LieIdeal.coe_derivedSeries_eq_intproof · cited by 1
- LieAlgebra.coe_derivedSeries_one_eqproof · cited by 1
- LieAlgebra.abelian_iff_derived_one_eq_botproof · cited by 1
- LieAlgebra.derivedSeriesOfIdeal_baseChangeproof · cited by 1
- LieIdeal.derivedSeries_map_eqproof · cited by 1
- LieIdeal.derivedSeries_map_leproof · cited by 1
- LieIdeal.derivedSeries_succ_eq_top_iffproof · cited by 1
- LieAlgebra.isSolvable_of_killingForm_apply_lie_eq_zeroproof · cited by 0