Theorems · Inductive type · nonassociative algebras

LieAlgebra.ofTwoCocycle

{R : Type u_5} →
  {L : Type u_6} →
    {M : Type u_7} →
      [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] → ↥(LieModule.Cohomology.twoCocycle R L M) → Type (max u_6 u_7)

A one-field structure giving a type synonym for a direct product. We use this to describe an alternative Lie algebra structure on the product, where the bracket is shifted by a 2-cocycle.

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

15 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModule