Theorems · Theorem · nonassociative algebras

LieSubalgebra.mem_engel_iff

∀ (R : Type u_1) {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (x y : L),
  y ∈ LieSubalgebra.engel R x ↔ ∃ n, ((LieAlgebra.ad R L) x ^ n) y = 0

Defined in

Mathlib.Algebra.Lie.EngelSubalgebra

Cited by

4 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebra