Theorems · Definition · nonassociative algebras

RootPairing.ofBilinear

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] →
          [Module.IsReflexive R M] →
            (B : M →ₗ[R] M →ₗ[R] R) →
              B.Nondegenerate → B.IsSymm → IsRegular 2 → RootPairing (↑{x | B.IsReflective x}) R M (Module.Dual R M)

The root pairing given by all reflective vectors for a bilinear form.

Defined in

Mathlib.LinearAlgebra.RootSystem.OfBilinear

Cited by

0 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.IsReflexive