Theorems · Definition · nonassociative algebras

LieModule.genWeightSpaceChain

{R : Type u_1} →
  {L : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : LieRing L] →
        [inst_2 : LieAlgebra R L] →
          (M : Type u_3) →
            [inst_3 : AddCommGroup M] →
              [inst_4 : Module R M] →
                [inst_5 : LieRingModule L M] →
                  [LieModule R L M] → [LieRing.IsNilpotent L] → (L → R) → (L → R) → ℤ → ℤ → LieSubmodule R L M

Given two (potential) weights χ₁ and χ₂ together with integers p and q, it is often useful to study the sum of weight spaces associated to the family of weights k • χ₁ + χ₂ for p < k < q.

Defined in

Mathlib.Algebra.Lie.Weights.Chain

Cited by

9 results in Mathlib

Foundations

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

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent