Theorems · Definition · nonassociative algebras

RootPairing.PolarizationEquiv

{ι : Type u_1} →
  {R : Type u_2} →
    {M : Type u_3} →
      {N : Type u_4} →
        [inst : Fintype ι] →
          [inst_1 : AddCommGroup M] →
            [inst_2 : AddCommGroup N] →
              [inst_3 : Field R] →
                [inst_4 : Module R M] →
                  [inst_5 : Module R N] → (P : RootPairing ι R M N) → [P.IsAnisotropic] → [P.IsRootSystem] → M ≃ₗ[R] N

The polarization map from weight space to coweight space as an equivalence.

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate

Cited by

6 results in Mathlib

Foundations

Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeAddCommGroupAddCommGroupFieldModuleModuleRootPairing.IsAnisotropicRootPairing.IsRootSystem