Theorems · Inductive type · nonassociative algebras

LieModule.Weight

(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] → Type (max u_2 u_3)

A weight of a Lie module is a map L → R such that the corresponding weight space is non-trivial.

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

172 results in Mathlib

Foundations

Depth 9 from the axioms, rests on 58 definitions · uses no axioms

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotent