Theorems · Inductive type · nonassociative algebras

LieDerivation

(R : Type u_1) →
  (L : Type u_2) →
    (M : Type u_3) →
      [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] → Type (max u_2 u_3)

A Lie derivation D from the Lie R-algebra L to the L-module M is an R-linear map that satisfies the Leibniz rule D [a, b] = [a, D b] - [b, D a].

Defined in

Mathlib.Algebra.Lie.Derivation.Basic

Cited by

95 results in Mathlib

Foundations

Depth 7 from the axioms, rests on 43 definitions · uses no axioms

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule