Theorems · Definition · nonassociative algebras

LieSubmodule.baseChange

{R : Type u_1} →
  (A : Type u_2) →
    {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] →
                      [inst_7 : CommRing A] →
                        [inst_8 : Algebra R A] →
                          LieSubmodule R L M → LieSubmodule A (TensorProduct R A L) (TensorProduct R A M)

If A is an R-algebra, any Lie submodule of a Lie module M with coefficients in R may be pushed forward to a Lie submodule of A ⊗ M with coefficients in A. This "base change" operation is also known as "extension of scalars".

Defined in

Mathlib.Algebra.Lie.BaseChange

Cited by

9 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleCommRingAlgebra