Theorems · Inductive type · nonassociative algebras

RootPairing.IsBalanced

{ι : Type u_1} →
  {R : Type u_2} →
    {M : Type u_3} →
      {N : Type u_4} →
        [inst : AddCommGroup M] →
          [inst_1 : AddCommGroup N] →
            [inst_2 : CommRing R] → [inst_3 : Module R M] → [inst_4 : Module R N] → RootPairing ι R M N → Prop

We say a root pairing is balanced if the root span and coroot span are perfectly complementary. All root systems are balanced and all finite root pairings over a field are balanced.

Defined in

Mathlib.LinearAlgebra.RootSystem.BaseChange

Cited by

6 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

AddCommGroupAddCommGroupCommRingModuleModule