Theorems · Definition · nonassociative algebras

RootPairing.EmbeddedG2.short

{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) → [self : P.EmbeddedG2] → ι

The distinguished short root of an embedded 𝔤₂ root pairing.

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.G2

Cited by

28 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

RootPairing.EmbeddedG2