Theorems · Theorem · nonassociative algebras
RootPairing.Base.algebraMap_cartanMatrixIn_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] (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),
(algebraMap S R) (RootPairing.Base.cartanMatrixIn S b i j) = P.pairing ↑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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- 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
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.Base.cartanMatrixIn_mul_diagonal_eqproof · cited by 2
- LieAlgebra.Basis.cartanMatrix_base_eqproof · cited by 0