Theorems · Theorem · nonassociative algebras

LieSubalgebra.isLieAbelian_lieSpan_iff

∀ {R : Type u_1} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {s : Set L},
  IsLieAbelian ↥(LieSubalgebra.lieSpan R L s) ↔ ∀ x ∈ s, ∀ y ∈ s, ⁅x, y⁆ = 0

Defined in

Mathlib.Algebra.Lie.Abelian

Cited by

1 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra