Theorems · Definition · nonassociative algebras

RootPairing.Base.toWeightBasis

{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} → (b : P.Base) → [P.IsRootSystem] → Module.Basis (↥b.support) R M

A base of a root system yields a basis of the root space.

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

8 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.IsRootSystem