Theorems · Theorem · group theory

Representation.Coinvariants.mem_ker_of_eq

∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommRing k] [inst_1 : Monoid G] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] {ρ : Representation k G V} (g : G) (x a : V),
  (ρ g) x - x = a → a ∈ Representation.Coinvariants.ker ρ

Defined in

Mathlib.RepresentationTheory.Coinvariants

Cited by

6 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

CommRingMonoidAddCommGroupModule