Theorems · Theorem · nonassociative algebras

LieAlgebra.mem_zeroRootSubalgebra

∀ (R : Type u_1) (L : Type u_2) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  (H : LieSubalgebra R L) [inst_3 : LieRing.IsNilpotent ↥H] (x : L),
  x ∈ LieAlgebra.zeroRootSubalgebra R L H ↔ ∀ (y : ↥H), ∃ k, ((LieModule.toEnd R (↥H) L) y ^ k) x = 0

Defined in

Mathlib.Algebra.Lie.Weights.Cartan

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRing.IsNilpotent