Theorems · Theorem · nonassociative algebras

RootPairing.GeckConstruction.basis_A_eq

∀ {ι : Type u_1} {K : Type u_2} {M : Type u_3} {N : Type u_4} [inst : Fintype ι] [inst_1 : DecidableEq ι]
  [inst_2 : Field K] [inst_3 : CharZero K] [inst_4 : AddCommGroup M] [inst_5 : Module K M] [inst_6 : AddCommGroup N]
  [inst_7 : Module K N] {P : RootPairing ι K M N} [inst_8 : P.IsReduced] [inst_9 : P.IsCrystallographic]
  [inst_10 : P.IsIrreducible] [inst_11 : P.IsRootSystem] (b : P.Base),
  (RootPairing.GeckConstruction.basis b).A = b.cartanMatrix

Defined in

Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basis

Cited by

0 results in Mathlib

Foundations

Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqFieldCharZeroAddCommGroupModuleAddCommGroupModuleRootPairing.IsReducedRootPairing.IsCrystallographicRootPairing.IsIrreducibleRootPairing.IsRootSystem