Theorems · Definition · nonassociative algebras

LieModule.shiftedGenWeightSpace.shift

(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] →
                  [inst_6 : LieModule R L M] →
                    [inst_7 : LieRing.IsNilpotent L] →
                      (χ : L → R) → ↥(LieModule.genWeightSpace M χ) ≃ₗ[R] ↥(LieModule.shiftedGenWeightSpace R L M χ)

Forgetting the action of L, the spaces genWeightSpace M χ and shiftedGenWeightSpace R L M χ are equivalent.

Defined in

Mathlib.Algebra.Lie.Weights.Linear

Cited by

4 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent