Theorems · Definition · nonassociative algebras
RootPairing.coreflection
{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] → RootPairing ι R M N → ι → N ≃ₗ[R] NThe reflection associated to a coroot.
- Defined in
- Mathlib.LinearAlgebra.RootSystem.Defs
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LinearEquivstatement · cited by 3,317
- RootPairingstatement and proof · cited by 710
- Module.reflectionproof · cited by 25
- RootPairing.root_coroot_twoproof · cited by 4
Cited by31
Results whose statement or proof uses this declaration.
- RootPairing.Equiv.reflectionproof · cited by 15
- RootPairing.coroot_reflectionPermstatement · cited by 9
- RootPairing.Equiv.reflection_invproof · cited by 5
- RootPairing.coreflection_apply_selfstatement · cited by 3
- RootPairing.toPerfPair_conj_reflectionstatement · cited by 2
- RootPairing.Equiv.reflection_coweightEquivstatement · cited by 2
- RootPairing.invtSubmodule_reflection_of_invtSubmodule_coreflectionstatement and proof · cited by 1
- RootPairing.smul_coroot_eq_of_root_eq_smulproof · cited by 1
- RootPairing.mapsTo_coreflection_corootstatement · cited by 1
- RootPairing.IsIrreducible.casesOnstatement and proof · cited by 1
- RootPairing.bijOn_coreflection_corootstatement · cited by 1
- RootPairing.pairing_smul_coroot_eqproof · cited by 1