Theorems · Definition · nonassociative algebras

RootPairing.Base.flip

{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.Base → P.flip.Base

Interchanging roots and coroots, one still has a base of a root pairing.

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

8 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule