Theorems · Theorem · nonassociative algebras

LieAlgebra.rootSpace_comap_eq_genWeightSpace

∀ {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] (χ : ↥H → R),
  LieSubmodule.comap H.incl' (LieAlgebra.rootSpace H χ) = LieModule.genWeightSpace (↥H) χ

Defined in

Mathlib.Algebra.Lie.Weights.Cartan

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRing.IsNilpotent