Theorems · Theorem · nonassociative algebras

LieAlgebra.Extension.lieModuleOf

∀ {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] [inst_5 : IsLieAbelian M] (E : LieAlgebra.Extension R M L),
  LieModule R L M

Given an extension of L by M whose kernel M is abelian, the kernel M gets an R-linear 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

3 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebraIsLieAbelian