Theorems · Theorem · group theory

Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination

∀ (k : Type u) {G : Type u} [inst : CommRing k] [inst_1 : CommGroup G] (g : G) [Finite G],
  (∀ (x : G), x ∈ Subgroup.zpowers g) →
    (Rep.Hom.hom ((Rep.leftRegular k G).applyAsHom g - CategoryTheory.CategoryStruct.id (Rep.leftRegular k G))).range =
      ((Finsupp.linearCombination k fun x => 1) ∘ₗ ↑(MonoidAlgebra.coeffLinearEquiv k)).ker

Defined in

Mathlib.RepresentationTheory.Homological.FiniteCyclic

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommGroupFinite