Theorems · Theorem · nonassociative algebras

RootPairing.chainBotCoeff_mul_chainTopCoeff.isNotG2

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [CharZero R] [IsDomain R]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : AddCommGroup N] [inst_6 : Module R N]
  {P : RootPairing ι R M N} [Finite ι] [P.IsCrystallographic] {b : P.Base} {i j k l m : ι} [P.IsReduced]
  [P.IsIrreducible],
  i ∈ b.support →
    j ∈ b.support →
      i ≠ j →
        P.root k + P.root i = P.root l →
          P.root k - P.root j = P.root m → P.root k + P.root i - P.root j ∈ Set.range ⇑P.root → P.IsNotG2

Defined in

Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCharZeroIsDomainAddCommGroupModuleAddCommGroupModuleFiniteRootPairing.IsCrystallographicRootPairing.IsReducedRootPairing.IsIrreducible