Theorems · Definition · group theory

Representation.IsSemisimpleRepresentation

{k : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      [inst : Monoid G] →
        [inst_1 : Field k] → [inst_2 : AddCommGroup V] → [inst_3 : Module k V] → Representation k G V → Prop

A representation is semisimple when every subrepresentation has a complement.

Defined in: Mathlib.RepresentationTheory.Semisimple
Cited by: 2 results in Mathlib
Foundations: Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid Field AddCommGroup Module

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Fieldstatement and proof · cited by 7,404
Monoidstatement and proof · cited by 3,887
Representationstatement and proof · cited by 396
ComplementedLatticeproof · cited by 30
Subrepresentationproof · cited by 23

Cited by2

Results whose statement or proof uses this declaration.

Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModulestatement and proof · cited by 0
Representation.isSemisimpleRepresentation_iff_isSemisimpleModule_asModulestatement and proof · cited by 0