Theorems · Inductive type · nonassociative algebras

LieModule.IsFaithful

(R : Type u) →
  (L : Type v) →
    (M : Type w) →
      [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] → Prop

A Lie module is faithful if the associated map L → End M is injective.

Defined in

Mathlib.Algebra.Lie.OfAssociative

Cited by

13 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule