Theorems · Theorem · nonassociative algebras

RootPairing.Base.abs_cartanMatrix_apply

∀ {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)
  [inst_5 : P.IsCrystallographic] [CharZero R] [IsDomain R] [Finite ι] [inst_9 : DecidableEq ι] {i j : ↥b.support},
  |b.cartanMatrix i j| = (if i = j then 4 else 0) - b.cartanMatrix i j

Defined in

Mathlib.LinearAlgebra.RootSystem.CartanMatrix

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleRootPairing.IsCrystallographicCharZeroIsDomainFiniteDecidableEq