Theorems · Inductive type · nonassociative algebras

RootPairing.IsReduced

{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] → RootPairing ι R M N → Prop

A root pairing is said to be reduced if any linearly dependent pair of roots is related by a sign. TODO Consider redefining this to make it perfectly symmetric between roots and coroots (i.e., so that the same demand is made of coroots) and turning RootPairing.instFlipIsReduced into a convenience constructor.

Defined in

Mathlib.LinearAlgebra.RootSystem.Reduced

Cited by

48 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

CommRingAddCommGroupModuleAddCommGroupModule