Theorems · Definition · group theory

groupHomology.mkH1OfIsTrivial

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] →
      (A : Rep.{u, u, u} k G) → [A.IsTrivial] → Additive (Abelianization G) →ₗ[ℤ] ↑A →ₗ[ℤ] ↑(groupHomology.H1 A)

If a G-representation on A is trivial, this is the natural map Gᵃᵇ → A → H₁(G, A) sending ⟦g⟧, a to ⟦single g a⟧.

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree

Cited by

3 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupRep.IsTrivial