Theorems · Theorem · nonassociative algebras

RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root

∀ {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] (P : RootPairing ι R M N) [inst_5 : Fintype ι]
  (i : ι),
  (4 • P.CoPolarization ∘ₗ P.Polarization) (P.root i) =
    ((P.RootForm (P.root i)) (P.root i) * (P.CorootForm (P.coroot i)) (P.coroot i)) • P.root i

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear

Cited by

0 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFintype