Theorems · Definition · nonassociative algebras

LieAlgebra.ofProd

{R : Type u_1} →
  {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] →
                    (c : ↥(LieModule.Cohomology.twoCocycle R L M)) → L × M ≃ LieAlgebra.ofTwoCocycle c

An equivalence between the direct product and the corresponding one-field structure. This is used to transfer the additive and scalar-multiple structure on the direct product to the type synonym.

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

11 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule