Theorems · Definition · nonassociative algebras
LieAlgebra.radical
(R : Type u) → (L : Type v) → [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → LieIdeal R L
The (solvable) radical of Lie algebra is the sSup of all solvable ideals.
- Defined in
- Mathlib.Algebra.Lie.Solvable
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, 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
- Set.ofPredproof · cited by 6,101
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- SupSet.sSupproof · cited by 954
- LieIdealstatement and proof · cited by 282
- LieAlgebra.IsSolvableproof · cited by 24
Cited by17
Results whose statement or proof uses this declaration.
- LieAlgebra.center_le_radicalstatement · cited by 2
- LieAlgebra.HasTrivialRadical.radical_eq_botstatement · cited by 2
- LieAlgebra.LieIdeal.solvable_iff_le_radicalstatement and proof · cited by 2
- LieAlgebra.HasCentralRadical.casesOnstatement and proof · cited by 1
- LieAlgebra.HasTrivialRadical.casesOnstatement and proof · cited by 1
- LieAlgebra.hasCentralRadical_iffstatement and proof · cited by 1
- LieAlgebra.hasTrivialRadical_iffstatement and proof · cited by 1
- LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithfulproof · cited by 1
- LieAlgebra.HasCentralRadical.radical_eq_centerstatement · cited by 0
- LieAlgebra.HasCentralRadical.recOnstatement and proof · cited by 0
- LieAlgebra.HasTrivialRadical.recOnstatement and proof · cited by 0
- LieAlgebra.radical_eq_top_of_isSolvablestatement · cited by 0