Theorems · Definition · nonassociative algebras

LieModule.genWeightSpace

{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] → [LieRing.IsNilpotent L] → (L → R) → LieSubmodule R L M

If M is a representation of a nilpotent Lie algebra L and χ : L → R is a family of scalars, then genWeightSpace M χ is the intersection of the maximal generalized χ x-eigenspaces of the action of x on M as x ranges over L. It is a Lie submodule because L is nilpotent.

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

99 results in Mathlib

Foundations

Depth 83 from the axioms, rests on 2,608 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent