Theorems · Definition · nonassociative algebras

RootPairing.EmbeddedG2.twoShortAddLong

{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) → [P.EmbeddedG2] → ι

The index of the root 2α + β where α is the short root and β is the long root.

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.G2

Cited by

5 results in Mathlib

Foundations

Depth 14 from the axioms · uses Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.EmbeddedG2