Theorems · Theorem · group theory

Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun

∀ {k G : Type u} [inst : CommRing k] [inst_1 : CommGroup G] [inst_2 : Fintype G] (A : Rep.{u, u, u} k G) (g : G)
  (hg : ∀ (x : G), x ∈ Subgroup.zpowers g) (i : ℕ) (a : ↑A) (x : MonoidAlgebra k G),
  (Rep.Hom.hom ((ModuleCat.Hom.hom ((Rep.FiniteCyclicGroup.homResolutionIso A g hg).inv.f i)) a)) x =
    x.coeff.sum fun x r => r • (A.ρ x) a

Defined in

Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic

Cited by

0 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommGroupFintype