Theorems · Definition · nonassociative algebras

LieAlgebra.Extension.ofTwoCocycle

{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 : LieRing M] →
              [inst_4 : LieAlgebra R M] →
                [IsLieAbelian M] →
                  [inst_6 : LieRingModule L M] →
                    [inst_7 : LieModule R L M] → ↥(LieModule.Cohomology.twoCocycle R L M) → LieAlgebra.Extension R M L

The extension of Lie algebras defined by a 2-cocycle.

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

3 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraIsLieAbelianLieRingModuleLieModule