Theorems · Theorem · nonassociative algebras

LieModule.toEnd_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] (x : L),
  (LieModule.toEnd A (TensorProduct R A L) (TensorProduct R A M)) (1 ⊗ₜ[R] x) =
    LinearMap.baseChange A ((LieModule.toEnd R L M) x)

Defined in

Mathlib.Algebra.Lie.BaseChange

Cited by

3 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleCommRingAlgebra