Theorems · Definition · nonassociative algebras

RootPairing.IsCrystallographic

{ι : Type u_1} →
  {R : Type u_2} →
    {M : Type u_4} →
      {N : Type u_5} →
        [inst : CommRing R] →
          [inst_1 : AddCommGroup M] →
            [inst_2 : Module R M] → [inst_3 : AddCommGroup N] → [inst_4 : Module R N] → RootPairing ι R M N → Prop

A root pairing is said to be crystallographic if the pairing between a root and coroot is always an integer.

Defined in

Mathlib.LinearAlgebra.RootSystem.IsValuedIn

Cited by

160 results in Mathlib

Foundations

Depth 41 from the axioms, rests on 572 definitions · uses propext, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule