Theorems · Theorem · nonassociative algebras
lie_abelian_iff_equiv_lie_abelian
∀ {R : Type u} {L₁ : Type v} {L₂ : Type w} [inst : CommRing R] [inst_1 : LieRing L₁] [inst_2 : LieRing L₂]
[inst_3 : LieAlgebra R L₁] [inst_4 : LieAlgebra R L₂] (e : L₁ ≃ₗ⁅R⁆ L₂), IsLieAbelian L₁ ↔ IsLieAbelian L₂- Defined in
- Mathlib.Algebra.Lie.Abelian
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
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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
- LieEquivstatement and proof · cited by 86
- IsLieAbelianstatement · cited by 55
- LieEquiv.symmproof · cited by 34
- LieEquiv.injectiveproof · cited by 3
- Function.Injective.isLieAbelianproof · cited by 2
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