Theorems · Definition · nonassociative algebras
LieAlgebra.maxNilpotentIdeal
(R : Type u) → (L : Type v) → [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : LieAlgebra R L] → LieSubmodule R L L
The max nilpotent ideal of a Lie algebra. It is defined as the max nilpotent Lie submodule of
L under the adjoint action.
- Defined in
- Mathlib.Algebra.Lie.Nilpotent
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 78 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.
Cites5
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
- LieSubmodulestatement · cited by 489
- LieModule.maxNilpotentSubmoduleproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- LieAlgebra.maxNilpotentIdeal_eq_top_of_isNilpotentstatement · cited by 0
- LieAlgebra.maxNilpotentIdeal_le_radicalstatement · cited by 0
- LieAlgebra.center_le_maxNilpotentIdealstatement · cited by 0
- LieAlgebra.LieIdeal.isNilpotent_iff_le_maxNilpotentIdealstatement · cited by 0