Theorems · Definition · nonassociative algebras
RootPairing.Hom.coweightHom
{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) → P.End →* (N →ₗ[R] N)ᵐᵒᵖThe coweight space representation of endomorphisms
- Defined in
- Mathlib.LinearAlgebra.RootSystem.Hom
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 49 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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- MonoidHomstatement · cited by 3,629
- MulOppositestatement · cited by 1,135
- RootPairingstatement and proof · cited by 710
- MulOpposite.opproof · cited by 520
- RootPairing.Hom.coweightMapproof · cited by 32
- RootPairing.Endstatement and proof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- RootPairing.Hom.coweightHom_injectivestatement and proof · cited by 1
- RootPairing.Equiv.coweightHom_toLinearMapstatement · cited by 1
- RootPairing.Equiv.coweightHom_injectiveproof · cited by 0