Theorems · Theorem · nonassociative algebras

RootPairing.EmbeddedG2.twoShortAddLongRoot_shortRoot

∀ {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 : P.EmbeddedG2] (B : P.InvariantForm),
  (B.form (RootPairing.EmbeddedG2.twoShortAddLongRoot P)) (RootPairing.EmbeddedG2.twoShortAddLongRoot P) =
    (B.form (RootPairing.EmbeddedG2.shortRoot P)) (RootPairing.EmbeddedG2.shortRoot P)

2α + β is short.

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.G2

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.EmbeddedG2