Theorems · Definition · nonassociative algebras

LieAlgebra.Extension.ringModuleOf

{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] → LieAlgebra.Extension R M L → LieRingModule L M

Given an extension of L by M whose kernel M is abelian, the kernel M gets an L-module structure. We do not make this an instance, because we may have to work with more than one extension.

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

7 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraIsLieAbelian