Theorems · Definition · nonassociative algebras

LieModule.shiftedGenWeightSpace

(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

A type synonym for the χ-weight space but with the action of x : L on m : genWeightSpace M χ, shifted to act as ⁅x, m⁆ - χ x • m.

Defined in

Mathlib.Algebra.Lie.Weights.Linear

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent