Theorems · Theorem · nonassociative algebras

RootPairing.restrictScalars_toLinearMap_apply_apply

∀ {ι : Type u_1} {L : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Field L] [inst_1 : AddCommGroup M]
  [inst_2 : AddCommGroup N] [inst_3 : Module L M] [inst_4 : Module L N] (P : RootPairing ι L M N) (K : Type u_5)
  [inst_5 : Field K] [inst_6 : Algebra K L] [inst_7 : Module K M] [inst_8 : Module K N] [inst_9 : IsScalarTower K L M]
  [inst_10 : IsScalarTower K L N] [inst_11 : P.IsBalanced] [inst_12 : P.IsValuedIn K]
  (x : ↥(Submodule.span K (Set.range ⇑P.root))) (y : ↥(Submodule.span K (Set.range ⇑P.coroot))),
  (algebraMap K L) (((P.restrictScalars' K).toLinearMap x) y) = (P.toLinearMap ↑x) ↑y

Defined in

Mathlib.LinearAlgebra.RootSystem.BaseChange

Cited by

1 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupAddCommGroupModuleModuleFieldAlgebraModuleModuleIsScalarTowerIsScalarTowerRootPairing.IsBalancedRootPairing.IsValuedIn