Theorems · Definition · nonassociative algebras

LieAlgebra.rootSpace

{R : Type u_1} →
  {L : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : LieRing L] →
        [inst_2 : LieAlgebra R L] →
          (H : LieSubalgebra R L) → [LieRing.IsNilpotent ↥H] → (↥H → R) → LieSubmodule R (↥H) L

Given a nilpotent Lie subalgebra H ⊆ L, the root space of a map χ : H → R is the weight space of L regarded as a module of H via the adjoint action.

Defined in

Mathlib.Algebra.Lie.Weights.Cartan

Cited by

74 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRing.IsNilpotent