Theorems · Theorem · nonassociative algebras

RootPairing.GeckConstruction.isSl2Triple

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Finite ι] [inst_1 : CommRing R]
  [inst_2 : IsDomain R] [inst_3 : CharZero R] [inst_4 : AddCommGroup M] [inst_5 : Module R M] [inst_6 : AddCommGroup N]
  [inst_7 : Module R N] {P : RootPairing ι R M N} [inst_8 : P.IsCrystallographic] {b : P.Base} [inst_9 : Fintype ι]
  (i : ↥b.support) [P.IsReduced] [inst_11 : DecidableEq ι],
  IsSl2Triple (RootPairing.GeckConstruction.h i) (RootPairing.GeckConstruction.e i) (RootPairing.GeckConstruction.f i)

Defined in

Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Relations

Cited by

0 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FiniteCommRingIsDomainCharZeroAddCommGroupModuleAddCommGroupModuleRootPairing.IsCrystallographicFintypeRootPairing.IsReducedDecidableEq