Theorems · Inductive type · nonassociative algebras

RootPairing.InvariantForm

{ι : Type u_1} →
  {R : Type u_2} →
    {M : Type u_4} →
      {N : Type u_5} →
        [inst : CommRing R] →
          [inst_1 : AddCommGroup M] →
            [inst_2 : Module R M] →
              [inst_3 : AddCommGroup N] → [inst_4 : Module R N] → RootPairing ι R M N → Type (max u_2 u_4)

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

Defined in

Mathlib.LinearAlgebra.RootSystem.RootPositive

Cited by

35 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

CommRingAddCommGroupModuleAddCommGroupModule