representation_theory.invariants | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

55b3f820

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

728ef9db

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -134,7 +134,7 @@ theorem averageMap_invariant (v : V) : averageMap ρ v ∈ invariants ρ := fun
 -/
 theorem averageMap_id (v : V) (hv : v ∈ invariants ρ) : averageMap ρ v = v :=
   by
-  rw [mem_invariants] at hv 
+  rw [mem_invariants] at hv
   simp [average, map_sum, hv, Finset.card_univ, nsmul_eq_smul_cast k _ v, smul_smul]
 #align representation.average_map_id Representation.averageMap_id
 -/

728ef9db

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Antoine Labelle. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Antoine Labelle
 -/
-import Mathbin.RepresentationTheory.Basic
-import Mathbin.RepresentationTheory.FdRep
+import RepresentationTheory.Basic
+import RepresentationTheory.FdRep
 
 #align_import representation_theory.invariants from "leanprover-community/mathlib"@"728ef9dbb281241906f25cbeb30f90d83e0bb451"

728ef9db

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Antoine Labelle. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Antoine Labelle
-
-! This file was ported from Lean 3 source module representation_theory.invariants
-! leanprover-community/mathlib commit 728ef9dbb281241906f25cbeb30f90d83e0bb451
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RepresentationTheory.Basic
 import Mathbin.RepresentationTheory.FdRep
 
+#align_import representation_theory.invariants from "leanprover-community/mathlib"@"728ef9dbb281241906f25cbeb30f90d83e0bb451"
+
 /-!
 # Subspace of invariants a group representation

728ef9db

bump to nightly-2023-07-04-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

05318d71

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Antoine Labelle
 
 ! This file was ported from Lean 3 source module representation_theory.invariants
-! leanprover-community/mathlib commit 55b3f8206b8596db8bb1804d8a92814a0b6670c9
+! leanprover-community/mathlib commit 728ef9dbb281241906f25cbeb30f90d83e0bb451
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RepresentationTheory.FdRep
 /-!
 # Subspace of invariants a group representation
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file introduces the subspace of invariants of a group representation
 and proves basic results about it.
 The main tool used is the average of all elements of the group, seen as an element of

55b3f820

bump to nightly-2023-07-02-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

a92db9c9

Diff

@@ -36,12 +36,15 @@ variable (k G : Type _) [CommSemiring k] [Group G]
 
 variable [Fintype G] [Invertible (Fintype.card G : k)]
 
+#print GroupAlgebra.average /-
 /-- The average of all elements of the group `G`, considered as an element of `monoid_algebra k G`.
 -/
 noncomputable def average : MonoidAlgebra k G :=
   ⅟ (Fintype.card G : k) • ∑ g : G, of k G g
 #align group_algebra.average GroupAlgebra.average
+-/
 
+#print GroupAlgebra.mul_average_left /-
 /-- `average k G` is invariant under left multiplication by elements of `G`.
 -/
 @[simp]
@@ -54,7 +57,9 @@ theorem mul_average_left (g : G) :
   show ⅟ ↑(Fintype.card G) • ∑ x : G, f (g * x) = ⅟ ↑(Fintype.card G) • ∑ x : G, f x
   rw [Function.Bijective.sum_comp (Group.mulLeft_bijective g) _]
 #align group_algebra.mul_average_left GroupAlgebra.mul_average_left
+-/
 
+#print GroupAlgebra.mul_average_right /-
 /-- `average k G` is invariant under right multiplication by elements of `G`.
 -/
 @[simp]
@@ -66,6 +71,7 @@ theorem mul_average_right (g : G) : average k G * Finsupp.single g 1 = average k
   show ⅟ ↑(Fintype.card G) • ∑ x : G, f (x * g) = ⅟ ↑(Fintype.card G) • ∑ x : G, f x
   rw [Function.Bijective.sum_comp (Group.mulRight_bijective g) _]
 #align group_algebra.mul_average_right GroupAlgebra.mul_average_right
+-/
 
 end GroupAlgebra
 
@@ -79,6 +85,7 @@ variable {k G V : Type _} [CommSemiring k] [Group G] [AddCommMonoid V] [Module k
 
 variable (ρ : Representation k G V)
 
+#print Representation.invariants /-
 /-- The subspace of invariants, consisting of the vectors fixed by all elements of `G`.
 -/
 def invariants : Submodule k V
@@ -88,31 +95,41 @@ def invariants : Submodule k V
   add_mem' v w hv hw g := by simp only [hv g, hw g, map_add]
   smul_mem' r v hv g := by simp only [hv g, LinearMap.map_smulₛₗ, RingHom.id_apply]
 #align representation.invariants Representation.invariants
+-/
 
+#print Representation.mem_invariants /-
 @[simp]
 theorem mem_invariants (v : V) : v ∈ invariants ρ ↔ ∀ g : G, ρ g v = v := by rfl
 #align representation.mem_invariants Representation.mem_invariants
+-/
 
+#print Representation.invariants_eq_inter /-
 theorem invariants_eq_inter : (invariants ρ).carrier = ⋂ g : G, Function.fixedPoints (ρ g) := by
   ext; simp [Function.IsFixedPt]
 #align representation.invariants_eq_inter Representation.invariants_eq_inter
+-/
 
 variable [Fintype G] [Invertible (Fintype.card G : k)]
 
+#print Representation.averageMap /-
 /-- The action of `average k G` gives a projection map onto the subspace of invariants.
 -/
 @[simp]
 noncomputable def averageMap : V →ₗ[k] V :=
   asAlgebraHom ρ (average k G)
 #align representation.average_map Representation.averageMap
+-/
 
+#print Representation.averageMap_invariant /-
 /-- The `average_map` sends elements of `V` to the subspace of invariants.
 -/
 theorem averageMap_invariant (v : V) : averageMap ρ v ∈ invariants ρ := fun g => by
   rw [average_map, ← as_algebra_hom_single_one, ← LinearMap.mul_apply, ← map_mul (as_algebra_hom ρ),
     mul_average_left]
 #align representation.average_map_invariant Representation.averageMap_invariant
+-/
 
+#print Representation.averageMap_id /-
 /-- The `average_map` acts as the identity on the subspace of invariants.
 -/
 theorem averageMap_id (v : V) (hv : v ∈ invariants ρ) : averageMap ρ v = v :=
@@ -120,10 +137,13 @@ theorem averageMap_id (v : V) (hv : v ∈ invariants ρ) : averageMap ρ v = v :
   rw [mem_invariants] at hv 
   simp [average, map_sum, hv, Finset.card_univ, nsmul_eq_smul_cast k _ v, smul_smul]
 #align representation.average_map_id Representation.averageMap_id
+-/
 
+#print Representation.isProj_averageMap /-
 theorem isProj_averageMap : LinearMap.IsProj ρ.invariants ρ.averageMap :=
   ⟨ρ.averageMap_invariant, ρ.averageMap_id⟩
 #align representation.is_proj_average_map Representation.isProj_averageMap
+-/
 
 end Invariants
 
@@ -137,6 +157,7 @@ section Rep
 
 variable {k : Type u} [CommRing k] {G : GroupCat.{u}}
 
+#print Representation.linHom.mem_invariants_iff_comm /-
 theorem mem_invariants_iff_comm {X Y : Rep k G} (f : X.V →ₗ[k] Y.V) (g : G) :
     (linHom X.ρ Y.ρ) g f = f ↔ f.comp (X.ρ g) = (Y.ρ g).comp f :=
   by
@@ -146,7 +167,9 @@ theorem mem_invariants_iff_comm {X Y : Rep k G} (f : X.V →ₗ[k] Y.V) (g : G)
     ρ_Aut_apply_hom]
   exact comm
 #align representation.lin_hom.mem_invariants_iff_comm Representation.linHom.mem_invariants_iff_comm
+-/
 
+#print Representation.linHom.invariantsEquivRepHom /-
 /-- The invariants of the representation `lin_hom X.ρ Y.ρ` correspond to the the representation
 homomorphisms from `X` to `Y` -/
 @[simps]
@@ -159,6 +182,7 @@ def invariantsEquivRepHom (X Y : Rep k G) : (linHom X.ρ Y.ρ).invariants ≃ₗ
   left_inv _ := by ext; rfl
   right_inv _ := by ext; rfl
 #align representation.lin_hom.invariants_equiv_Rep_hom Representation.linHom.invariantsEquivRepHom
+-/
 
 end Rep
 
@@ -166,6 +190,7 @@ section FdRep
 
 variable {k : Type u} [Field k] {G : GroupCat.{u}}
 
+#print Representation.linHom.invariantsEquivFdRepHom /-
 /-- The invariants of the representation `lin_hom X.ρ Y.ρ` correspond to the the representation
 homomorphisms from `X` to `Y` -/
 def invariantsEquivFdRepHom (X Y : FdRep k G) : (linHom X.ρ Y.ρ).invariants ≃ₗ[k] X ⟶ Y :=
@@ -173,6 +198,7 @@ def invariantsEquivFdRepHom (X Y : FdRep k G) : (linHom X.ρ Y.ρ).invariants 
   rw [← FdRep.forget₂_ρ, ← FdRep.forget₂_ρ]
   exact lin_hom.invariants_equiv_Rep_hom _ _ ≪≫ₗ FdRep.forget₂HomLinearEquiv X Y
 #align representation.lin_hom.invariants_equiv_fdRep_hom Representation.linHom.invariantsEquivFdRepHom
+-/
 
 end FdRep

55b3f820

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -51,7 +51,7 @@ theorem mul_average_left (g : G) :
   simp only [mul_one, Finset.mul_sum, Algebra.mul_smul_comm, average, MonoidAlgebra.of_apply,
     Finset.sum_congr, MonoidAlgebra.single_mul_single]
   set f : G → MonoidAlgebra k G := fun x => Finsupp.single x 1
-  show (⅟ ↑(Fintype.card G) • ∑ x : G, f (g * x)) = ⅟ ↑(Fintype.card G) • ∑ x : G, f x
+  show ⅟ ↑(Fintype.card G) • ∑ x : G, f (g * x) = ⅟ ↑(Fintype.card G) • ∑ x : G, f x
   rw [Function.Bijective.sum_comp (Group.mulLeft_bijective g) _]
 #align group_algebra.mul_average_left GroupAlgebra.mul_average_left
 
@@ -63,7 +63,7 @@ theorem mul_average_right (g : G) : average k G * Finsupp.single g 1 = average k
   simp only [mul_one, Finset.sum_mul, Algebra.smul_mul_assoc, average, MonoidAlgebra.of_apply,
     Finset.sum_congr, MonoidAlgebra.single_mul_single]
   set f : G → MonoidAlgebra k G := fun x => Finsupp.single x 1
-  show (⅟ ↑(Fintype.card G) • ∑ x : G, f (x * g)) = ⅟ ↑(Fintype.card G) • ∑ x : G, f x
+  show ⅟ ↑(Fintype.card G) • ∑ x : G, f (x * g) = ⅟ ↑(Fintype.card G) • ∑ x : G, f x
   rw [Function.Bijective.sum_comp (Group.mulRight_bijective g) _]
 #align group_algebra.mul_average_right GroupAlgebra.mul_average_right

55b3f820

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -117,7 +117,7 @@ theorem averageMap_invariant (v : V) : averageMap ρ v ∈ invariants ρ := fun
 -/
 theorem averageMap_id (v : V) (hv : v ∈ invariants ρ) : averageMap ρ v = v :=
   by
-  rw [mem_invariants] at hv
+  rw [mem_invariants] at hv 
   simp [average, map_sum, hv, Finset.card_univ, nsmul_eq_smul_cast k _ v, smul_smul]
 #align representation.average_map_id Representation.averageMap_id

55b3f820

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -24,7 +24,7 @@ results that the order of `G` is invertible in `k` (e. g. `k` has characteristic
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 open MonoidAlgebra

55b3f820

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -93,10 +93,8 @@ def invariants : Submodule k V
 theorem mem_invariants (v : V) : v ∈ invariants ρ ↔ ∀ g : G, ρ g v = v := by rfl
 #align representation.mem_invariants Representation.mem_invariants
 
-theorem invariants_eq_inter : (invariants ρ).carrier = ⋂ g : G, Function.fixedPoints (ρ g) :=
-  by
-  ext
-  simp [Function.IsFixedPt]
+theorem invariants_eq_inter : (invariants ρ).carrier = ⋂ g : G, Function.fixedPoints (ρ g) := by
+  ext; simp [Function.IsFixedPt]
 #align representation.invariants_eq_inter Representation.invariants_eq_inter
 
 variable [Fintype G] [Invertible (Fintype.card G : k)]
@@ -158,12 +156,8 @@ def invariantsEquivRepHom (X Y : Rep k G) : (linHom X.ρ Y.ρ).invariants ≃ₗ
   map_add' _ _ := rfl
   map_smul' _ _ := rfl
   invFun f := ⟨f.hom, fun g => (mem_invariants_iff_comm _ g).2 (f.comm g)⟩
-  left_inv _ := by
-    ext
-    rfl
-  right_inv _ := by
-    ext
-    rfl
+  left_inv _ := by ext; rfl
+  right_inv _ := by ext; rfl
 #align representation.lin_hom.invariants_equiv_Rep_hom Representation.linHom.invariantsEquivRepHom
 
 end Rep

55b3f820

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

55b3f820

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -31,7 +31,6 @@ open Representation
 namespace GroupAlgebra
 
 variable (k G : Type*) [CommSemiring k] [Group G]
-
 variable [Fintype G] [Invertible (Fintype.card G : k)]
 
 /-- The average of all elements of the group `G`, considered as an element of `MonoidAlgebra k G`.
@@ -71,7 +70,6 @@ section Invariants
 open GroupAlgebra
 
 variable {k G V : Type*} [CommSemiring k] [Group G] [AddCommMonoid V] [Module k V]
-
 variable (ρ : Representation k G V)
 
 /-- The subspace of invariants, consisting of the vectors fixed by all elements of `G`.

55b3f820

feat(RepresentationTheory/GroupCohomology/LowDegree): H¹(G, A) ≃ Hom(G, A) for a trivial representation (#7988)

2852d235

Diff

@@ -91,6 +91,10 @@ theorem invariants_eq_inter : (invariants ρ).carrier = ⋂ g : G, Function.fixe
   ext; simp [Function.IsFixedPt]
 #align representation.invariants_eq_inter Representation.invariants_eq_inter
 
+theorem invariants_eq_top [ρ.IsTrivial] :
+    invariants ρ = ⊤ :=
+eq_top_iff.2 (fun x _ g => ρ.apply_eq_self g x)
+
 variable [Fintype G] [Invertible (Fintype.card G : k)]
 
 /-- The action of `average k G` gives a projection map onto the subspace of invariants.

55b3f820

feat: use suppress_compilation in tensor products (#7504)

More principled version of #7281.

9ff5b6f1

Diff

@@ -20,6 +20,7 @@ In order for the definition of the average element to make sense, we need to ass
 results that the order of `G` is invertible in `k` (e. g. `k` has characteristic `0`).
 -/
 
+suppress_compilation
 
 open scoped BigOperators

55b3f820

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -29,7 +29,7 @@ open Representation
 
 namespace GroupAlgebra
 
-variable (k G : Type _) [CommSemiring k] [Group G]
+variable (k G : Type*) [CommSemiring k] [Group G]
 
 variable [Fintype G] [Invertible (Fintype.card G : k)]
 
@@ -69,7 +69,7 @@ section Invariants
 
 open GroupAlgebra
 
-variable {k G V : Type _} [CommSemiring k] [Group G] [AddCommMonoid V] [Module k V]
+variable {k G V : Type*} [CommSemiring k] [Group G] [AddCommMonoid V] [Module k V]
 
 variable (ρ : Representation k G V)

55b3f820

chore: fix grammar mistakes (#6121)

a16538af

Diff

@@ -138,7 +138,7 @@ theorem mem_invariants_iff_comm {X Y : Rep k G} (f : X.V →ₗ[k] Y.V) (g : G)
   exact comm
 #align representation.lin_hom.mem_invariants_iff_comm Representation.linHom.mem_invariants_iff_comm
 
-/-- The invariants of the representation `linHom X.ρ Y.ρ` correspond to the the representation
+/-- The invariants of the representation `linHom X.ρ Y.ρ` correspond to the representation
 homomorphisms from `X` to `Y`. -/
 @[simps]
 def invariantsEquivRepHom (X Y : Rep k G) : (linHom X.ρ Y.ρ).invariants ≃ₗ[k] X ⟶ Y where
@@ -157,7 +157,7 @@ section FdRep
 
 variable {k : Type u} [Field k] {G : GroupCat.{u}}
 
-/-- The invariants of the representation `linHom X.ρ Y.ρ` correspond to the the representation
+/-- The invariants of the representation `linHom X.ρ Y.ρ` correspond to the representation
 homomorphisms from `X` to `Y`. -/
 def invariantsEquivFdRepHom (X Y : FdRep k G) : (linHom X.ρ Y.ρ).invariants ≃ₗ[k] X ⟶ Y := by
   rw [← FdRep.forget₂_ρ, ← FdRep.forget₂_ρ]

55b3f820

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Antoine Labelle. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Antoine Labelle
-
-! This file was ported from Lean 3 source module representation_theory.invariants
-! leanprover-community/mathlib commit 55b3f8206b8596db8bb1804d8a92814a0b6670c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RepresentationTheory.Basic
 import Mathlib.RepresentationTheory.FdRep
 
+#align_import representation_theory.invariants from "leanprover-community/mathlib"@"55b3f8206b8596db8bb1804d8a92814a0b6670c9"
+
 /-!
 # Subspace of invariants a group representation

55b3f820

feat: port RepresentationTheory.Invariants (#5655)

9dd08868

`representation_theory.invariants` ⟷ `Mathlib.RepresentationTheory.Invariants`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 879

representation_theory.invariants ⟷ Mathlib.RepresentationTheory.Invariants

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 879

`representation_theory.invariants` ⟷ `Mathlib.RepresentationTheory.Invariants`