Theorems · Definition · nonassociative algebras

LieModule.chainBotCoeff

{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] →
                  [inst_6 : LieModule R L M] →
                    [inst_7 : LieRing.IsNilpotent L] →
                      [IsAddTorsionFree R] →
                        [IsDomain R] →
                          [Module.IsTorsionFree R M] → [IsNoetherian R M] → (L → R) → LieModule.Weight R L M → ℕ

This is the largest n : ℕ such that -i • α + β is a weight for all 0 ≤ i ≤ n.

Defined in

Mathlib.Algebra.Lie.Weights.Chain

Cited by

22 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotentIsAddTorsionFreeIsDomainModule.IsTorsionFreeIsNoetherian