Theorems · Theorem · nonassociative algebras

RootPairing.Base.cartanMatrixIn_nondegenerate

∀ {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] (S : Type u_5) [inst_5 : CommRing S]
  [inst_6 : Algebra S R] [IsDomain R] [NeZero 2] [FaithfulSMul S R] [IsDomain S] {P : RootPairing ι R M N}
  [P.IsRootSystem] [inst_12 : P.IsValuedIn S] [inst_13 : Fintype ι] [P.IsAnisotropic] (b : P.Base),
  (RootPairing.Base.cartanMatrixIn S b).Nondegenerate

Defined in

Mathlib.LinearAlgebra.RootSystem.CartanMatrix

Cited by

1 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCommRingAlgebraIsDomainNeZeroFaithfulSMulIsDomainRootPairing.IsRootSystemRootPairing.IsValuedInFintypeRootPairing.IsAnisotropic