Skip to content

Commit

Permalink
fix PR comments
Browse files Browse the repository at this point in the history
  • Loading branch information
javierlcontreras committed Dec 20, 2024
1 parent bbffc51 commit 04dabf4
Showing 1 changed file with 4 additions and 8 deletions.
12 changes: 4 additions & 8 deletions FLT/Deformations/RepresentationTheory/Irreducible.lean
Original file line number Diff line number Diff line change
Expand Up @@ -10,23 +10,19 @@ variable {k : Type*} [Field k]
variable {W : Type*} [AddCommMonoid W] [Module k W]

/-!
IsIrreducible predicates that a given Representation ρ is irreducible (also known as simple),
IsIrreducible ρ is the statement that a given Representation ρ is irreducible (also known as simple),
meaning that any subrepresentation must be either the full one (⊤) or zero (⊥)
This notion is only well behaved when the representation is over a field k. If it were defined over
a ring A with a nontrivial ideal J, the subrepresentation JW would be a non trivial subrepresentation,
so ρ would never be irreducible.
a ring A with a nontrivial ideal J, the subrepresentation JW would often be a non trivial subrepresentation,
so ρ would rarely be irreducible.
-/
class IsIrreducible (ρ : Representation k G W) : Prop where
irreducible : IsSimpleOrder (Subrepresentation ρ)

/-!
IsAbsolutelyIrreducible predicates that a given Representation ρ over a field k
IsAbsolutelyIrreducible ρ states that a given Representation ρ over a field k
is absolutely irreducible, meaning that all the possible base change extensions are irreducible.
This notion is only well behaved when the representation is over a field k. If it were defined over
a ring A with a nontrivial ideal J, the subrepresentation JW would be a non trivial subrepresentation,
so ρ would never be absolutely irreducible.
-/
class IsAbsolutelyIrreducible (ρ : Representation k G W) : Prop where
absolutelyIrreducible : ∀ k', ∀ _ : Field k', ∀ _ : Algebra k k', IsIrreducible (k' ⊗ᵣ' ρ)
Expand Down

0 comments on commit 04dabf4

Please sign in to comment.