Theorems · Theorem · nonassociative algebras
RootPairing.Base.cartanMatrixIn_def
∀ {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} [inst_7 : P.IsValuedIn S] (b : P.Base) (i j : ↥b.support),
RootPairing.Base.cartanMatrixIn S b i j = P.pairingIn S ↑i ↑j- Cited by
- 2 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- Finsetstatement · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- RootPairingstatement and proof · cited by 710
- RootPairing.Basestatement and proof · cited by 148
- RootPairing.Base.supportstatement and proof · cited by 139
- RootPairing.IsValuedInstatement and proof · cited by 108
- RootPairing.pairingInstatement · cited by 100
- RootPairing.Base.cartanMatrixInstatement · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.Base.cartanMatrix_apply_eq_zero_iff_pairingproof · cited by 1
- RootPairing.Base.cartanMatrix_eq_neg_chainTopCoeffproof · cited by 1