Theorems · Theorem · nonassociative algebras
lie_eq_self_of_isAtom_of_nonabelian
∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L),
IsAtom I → ¬IsLieAbelian ↥I → ⁅I, I⁆ = I- Defined in
- Mathlib.Algebra.Lie.Abelian
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 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.
Cites10
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 · cited by 642
- LieIdealstatement and proof · cited by 282
- IsAtomstatement and proof · cited by 130
- not_imp_notproof · cited by 63
- IsLieAbelianstatement and proof · cited by 55
- LieSubmodule.lie_abelian_iff_lie_self_eq_botproof · cited by 3
- lie_eq_self_of_isAtom_of_ne_botproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.InvariantForm.orthogonal_disjointproof · cited by 3
- LieAlgebra.InvariantForm.isSemisimple_of_nondegenerateproof · cited by 0