Theorems · Theorem · nonassociative algebras

RootPairing.EmbeddedG2.ofPairingInThree_long

∀ {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) [inst_5 : CharZero R]
  [inst_6 : P.IsCrystallographic] [inst_7 : P.IsReduced] (long short : ι) (h : P.pairingIn ℤ long short = 3),
  RootPairing.EmbeddedG2.long P = (P.reflectionPerm long) long

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.G2

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCharZeroRootPairing.IsCrystallographicRootPairing.IsReduced