Theorems · Inductive type · nonassociative algebras

RootPairing.RootPositiveForm

{ι : Type u_1} →
  {R : Type u_2} →
    (S : Type u_3) →
      {M : Type u_4} →
        {N : Type u_5} →
          [inst : CommRing S] →
            [LinearOrder S] →
              [inst_2 : CommRing R] →
                [inst_3 : Algebra S R] →
                  [inst_4 : AddCommGroup M] →
                    [inst_5 : Module R M] →
                      [inst_6 : AddCommGroup N] →
                        [inst_7 : Module R N] → (P : RootPairing ι R M N) → [P.IsValuedIn S] → Type (max u_2 u_4)

Given a root pairing, this is an invariant symmetric bilinear form satisfying a positivity condition.

Defined in

Mathlib.LinearAlgebra.RootSystem.RootPositive

Cited by

32 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

CommRingLinearOrderCommRingAlgebraAddCommGroupModuleAddCommGroupModuleRootPairing.IsValuedIn