Theorems · Definition · nonassociative algebras

RootPairing.GeckConstruction.f

{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.IsCrystallographic] →
                      {b : P.Base} →
                        [Finite ι] →
                          [IsDomain R] → [CharZero R] → ↥b.support → Matrix (↥b.support ⊕ ι) (↥b.support ⊕ ι) R

Part of an sl₂ triple used in Geck's construction of a Lie algebra from a root system.

Defined in

Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic

Cited by

18 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.IsCrystallographicFiniteIsDomainCharZero