Theorems · Definition · group theory

Representation.averageMap

{k : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      [inst : CommRing k] →
        [inst_1 : Group G] →
          [inst_2 : AddCommGroup V] →
            [inst_3 : Module k V] →
              Representation k G V → [inst_4 : Fintype G] → [Invertible ↑(Fintype.card G)] → V →ₗ[k] V

The action of average k G gives a projection map onto the subspace of invariants.

Defined in

Mathlib.RepresentationTheory.Invariants

Cited by

3 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupAddCommGroupModuleFintypeInvertible