Theorems · Theorem · nonassociative algebras

RootPairing.Hom.weight_coweight_transpose

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] {ι₂ : Type u_5} {M₂ : Type u_6} {N₂ : Type u_7}
  [inst_5 : AddCommGroup M₂] [inst_6 : Module R M₂] [inst_7 : AddCommGroup N₂] [inst_8 : Module R N₂]
  {P : RootPairing ι R M N} {Q : RootPairing ι₂ R M₂ N₂} (self : P.Hom Q),
  self.weightMap.dualMap ∘ₗ ↑Q.flip.toPerfPair = ↑P.flip.toPerfPair ∘ₗ self.coweightMap

Defined in

Mathlib.LinearAlgebra.RootSystem.Hom

Cited by

2 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleAddCommGroupModuleAddCommGroupModule