Theorems · Definition · nonassociative algebras

RootPairing.Base.cartanMatrixIn

{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] →
                        {P : RootPairing ι R M N} → [P.IsValuedIn S] → (b : P.Base) → Matrix (↥b.support) (↥b.support) S

The Cartan matrix of a root pairing, taking values in S, with respect to a base b. See also RootPairing.Base.cartanMatrix.

Defined in

Mathlib.LinearAlgebra.RootSystem.CartanMatrix

Cited by

7 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCommRingAlgebraRootPairing.IsValuedIn