Theorems · Theorem · nonassociative algebras

LieAlgebra.eq_rootSpace_zero_iff_isCartan

∀ (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] [IsNoetherian R L],
  H.toLieSubmodule = LieAlgebra.rootSpace H 0 ↔ H.IsCartanSubalgebra

Defined in

Mathlib.Algebra.Lie.Weights.Cartan

Cited by

1 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRing.IsNilpotentIsNoetherian