Theorems · Definition · nonassociative algebras

RootPairing.EmbeddedG2.indexEquivAllRoots

{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] →
                      [Finite ι] →
                        [CharZero R] →
                          [IsDomain R] → [P.IsIrreducible] → ι ≃ ↥(RootPairing.EmbeddedG2.allRoots P).toFinset

The natural labelling of RootPairing.EmbeddedG2.allRoots.

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.G2

Cited by

3 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.EmbeddedG2FiniteCharZeroIsDomainRootPairing.IsIrreducible