Theorems · Theorem · group theory
Representation.irreducible_iff_isSimpleModule_asModule
∀ {G : Type u_1} {k : Type u_2} {V : Type u_3} [inst : Monoid G] [inst_1 : Field k] [inst_2 : AddCommGroup V]
[inst_3 : Module k V] (ρ : Representation k G V), ρ.IsIrreducible ↔ IsSimpleModule (MonoidAlgebra k G) ρ.asModule- Defined in
- Mathlib.RepresentationTheory.Irreducible
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- MonoidAlgebrastatement and proof · cited by 590
- Representationstatement and proof · cited by 396
- IsSimpleModulestatement · cited by 114
- Representation.asModulestatement and proof · cited by 22
- isSimpleModule_iffproof · cited by 12
- OrderIso.isSimpleOrder_iffproof · cited by 12
- Representation.IsIrreduciblestatement and proof · cited by 10
- Subrepresentation.subrepresentationSubmoduleOrderIsoproof · cited by 4
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