Theorems · Theorem · nonassociative algebras

RootPairing.coxeterWeightIn_eq_zero_iff

∀ {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] (P : RootPairing ι R M N) [CharZero R]
  [inst_6 : P.IsCrystallographic] (i j : ι) [IsDomain R], P.coxeterWeightIn ℤ i j = 0 ↔ P.pairingIn ℤ i j = 0

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCharZeroRootPairing.IsCrystallographicIsDomain