Theorems · Definition · nonassociative algebras

LieModule.genWeightSpaceOf

{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] → R → L → LieSubmodule R L M

If M is a representation of a nilpotent Lie algebra L, χ is a scalar, and x : L, then genWeightSpaceOf M χ x is the maximal generalized χ-eigenspace of the action of x on M. It is a Lie submodule because L is nilpotent.

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

17 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent