Theorems · Definition · nonassociative algebras

LieModule.weightSpace

{R : Type u_2} →
  {L : Type u_3} →
    (M : Type u_4) →
      [inst : CommRing R] →
        [inst_1 : LieRing L] →
          [inst_2 : LieAlgebra R L] →
            [inst_3 : AddCommGroup M] →
              [inst_4 : Module R M] → [inst_5 : LieRingModule L M] → [LieModule R L M] → (L → R) → LieSubmodule R L M

If M is a representation of a Lie algebra L and χ : L → R is a family of scalars, then weightSpace M χ is the intersection of the χ x-eigenspaces of the action of x on M as x ranges over L.

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

7 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule