Theorems · Definition · nonassociative algebras

LieModule.Weight.IsZero

{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] → LieModule.Weight R L M → Prop

The proposition that a weight of a Lie module is zero. We make this definition because we cannot define a Zero (Weight R L M) instance since the weight space of the zero function can be trivial.

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

31 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent