algebra.lie.characterMathlib.Algebra.Lie.Character

This file has been ported!

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

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -57,7 +57,7 @@ theorem lieCharacter_apply_of_mem_derived (χ : LieCharacter R L) {x : L}
     (h : x ∈ derivedSeries R L 1) : χ x = 0 :=
   by
   rw [derived_series_def, derived_series_of_ideal_succ, derived_series_of_ideal_zero, ←
-    LieSubmodule.mem_coeSubmodule, LieSubmodule.lieIdeal_oper_eq_linear_span] at h 
+    LieSubmodule.mem_coeSubmodule, LieSubmodule.lieIdeal_oper_eq_linear_span] at h
   apply Submodule.span_induction h
   · rintro y ⟨⟨z, hz⟩, ⟨⟨w, hw⟩, rfl⟩⟩; apply lie_character_apply_lie
   · exact χ.map_zero
Diff
@@ -3,9 +3,9 @@ Copyright (c) 2021 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
-import Mathbin.Algebra.Lie.Abelian
-import Mathbin.Algebra.Lie.Solvable
-import Mathbin.LinearAlgebra.Dual
+import Algebra.Lie.Abelian
+import Algebra.Lie.Solvable
+import LinearAlgebra.Dual
 
 #align_import algebra.lie.character from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
 
Diff
@@ -2,16 +2,13 @@
 Copyright (c) 2021 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module algebra.lie.character
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Lie.Abelian
 import Mathbin.Algebra.Lie.Solvable
 import Mathbin.LinearAlgebra.Dual
 
+#align_import algebra.lie.character from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
 /-!
 # Characters of Lie algebras
 
Diff
@@ -48,10 +48,12 @@ abbrev LieCharacter :=
 
 variable {R L}
 
+#print LieAlgebra.lieCharacter_apply_lie /-
 @[simp]
 theorem lieCharacter_apply_lie (χ : LieCharacter R L) (x y : L) : χ ⁅x, y⁆ = 0 := by
   rw [LieHom.map_lie, LieRing.of_associative_ring_bracket, mul_comm, sub_self]
 #align lie_algebra.lie_character_apply_lie LieAlgebra.lieCharacter_apply_lie
+-/
 
 #print LieAlgebra.lieCharacter_apply_of_mem_derived /-
 theorem lieCharacter_apply_of_mem_derived (χ : LieCharacter R L) {x : L}
@@ -67,6 +69,7 @@ theorem lieCharacter_apply_of_mem_derived (χ : LieCharacter R L) {x : L}
 #align lie_algebra.lie_character_apply_of_mem_derived LieAlgebra.lieCharacter_apply_of_mem_derived
 -/
 
+#print LieAlgebra.lieCharacterEquivLinearDual /-
 /-- For an Abelian Lie algebra, characters are just linear forms. -/
 @[simps]
 def lieCharacterEquivLinearDual [IsLieAbelian L] : LieCharacter R L ≃ Module.Dual R L
@@ -80,6 +83,7 @@ def lieCharacterEquivLinearDual [IsLieAbelian L] : LieCharacter R L ≃ Module.D
   left_inv χ := by ext; rfl
   right_inv ψ := by ext; rfl
 #align lie_algebra.lie_character_equiv_linear_dual LieAlgebra.lieCharacterEquivLinearDual
+-/
 
 end LieAlgebra
 
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module algebra.lie.character
-! leanprover-community/mathlib commit 132328c4dd48da87adca5d408ca54f315282b719
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.Dual
 /-!
 # Characters of Lie algebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A character of a Lie algebra `L` over a commutative ring `R` is a morphism of Lie algebras `L → R`,
 where `R` is regarded as a Lie algebra over itself via the ring commutator. For an Abelian Lie
 algebra (e.g., a Cartan subalgebra of a semisimple Lie algebra) a character is just a linear form.
Diff
@@ -36,10 +36,12 @@ namespace LieAlgebra
 
 variable (R : Type u) (L : Type v) [CommRing R] [LieRing L] [LieAlgebra R L]
 
+#print LieAlgebra.LieCharacter /-
 /-- A character of a Lie algebra is a morphism to the scalars. -/
 abbrev LieCharacter :=
   L →ₗ⁅R⁆ R
 #align lie_algebra.lie_character LieAlgebra.LieCharacter
+-/
 
 variable {R L}
 
@@ -48,6 +50,7 @@ theorem lieCharacter_apply_lie (χ : LieCharacter R L) (x y : L) : χ ⁅x, y⁆
   rw [LieHom.map_lie, LieRing.of_associative_ring_bracket, mul_comm, sub_self]
 #align lie_algebra.lie_character_apply_lie LieAlgebra.lieCharacter_apply_lie
 
+#print LieAlgebra.lieCharacter_apply_of_mem_derived /-
 theorem lieCharacter_apply_of_mem_derived (χ : LieCharacter R L) {x : L}
     (h : x ∈ derivedSeries R L 1) : χ x = 0 :=
   by
@@ -59,6 +62,7 @@ theorem lieCharacter_apply_of_mem_derived (χ : LieCharacter R L) {x : L}
   · intro y z hy hz; rw [LieHom.map_add, hy, hz, add_zero]
   · intro t y hy; rw [LieHom.map_smul, hy, smul_zero]
 #align lie_algebra.lie_character_apply_of_mem_derived LieAlgebra.lieCharacter_apply_of_mem_derived
+-/
 
 /-- For an Abelian Lie algebra, characters are just linear forms. -/
 @[simps]
Diff
@@ -52,7 +52,7 @@ theorem lieCharacter_apply_of_mem_derived (χ : LieCharacter R L) {x : L}
     (h : x ∈ derivedSeries R L 1) : χ x = 0 :=
   by
   rw [derived_series_def, derived_series_of_ideal_succ, derived_series_of_ideal_zero, ←
-    LieSubmodule.mem_coeSubmodule, LieSubmodule.lieIdeal_oper_eq_linear_span] at h
+    LieSubmodule.mem_coeSubmodule, LieSubmodule.lieIdeal_oper_eq_linear_span] at h 
   apply Submodule.span_induction h
   · rintro y ⟨⟨z, hz⟩, ⟨⟨w, hw⟩, rfl⟩⟩; apply lie_character_apply_lie
   · exact χ.map_zero
Diff
@@ -54,13 +54,10 @@ theorem lieCharacter_apply_of_mem_derived (χ : LieCharacter R L) {x : L}
   rw [derived_series_def, derived_series_of_ideal_succ, derived_series_of_ideal_zero, ←
     LieSubmodule.mem_coeSubmodule, LieSubmodule.lieIdeal_oper_eq_linear_span] at h
   apply Submodule.span_induction h
-  · rintro y ⟨⟨z, hz⟩, ⟨⟨w, hw⟩, rfl⟩⟩
-    apply lie_character_apply_lie
+  · rintro y ⟨⟨z, hz⟩, ⟨⟨w, hw⟩, rfl⟩⟩; apply lie_character_apply_lie
   · exact χ.map_zero
-  · intro y z hy hz
-    rw [LieHom.map_add, hy, hz, add_zero]
-  · intro t y hy
-    rw [LieHom.map_smul, hy, smul_zero]
+  · intro y z hy hz; rw [LieHom.map_add, hy, hz, add_zero]
+  · intro t y hy; rw [LieHom.map_smul, hy, smul_zero]
 #align lie_algebra.lie_character_apply_of_mem_derived LieAlgebra.lieCharacter_apply_of_mem_derived
 
 /-- For an Abelian Lie algebra, characters are just linear forms. -/
@@ -73,12 +70,8 @@ def lieCharacterEquivLinearDual [IsLieAbelian L] : LieCharacter R L ≃ Module.D
       map_lie' := fun x y => by
         rw [LieModule.IsTrivial.trivial, LieRing.of_associative_ring_bracket, mul_comm, sub_self,
           LinearMap.toFun_eq_coe, LinearMap.map_zero] }
-  left_inv χ := by
-    ext
-    rfl
-  right_inv ψ := by
-    ext
-    rfl
+  left_inv χ := by ext; rfl
+  right_inv ψ := by ext; rfl
 #align lie_algebra.lie_character_equiv_linear_dual LieAlgebra.lieCharacterEquivLinearDual
 
 end LieAlgebra

Changes in mathlib4

mathlib3
mathlib4
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

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

Diff
@@ -2,16 +2,13 @@
 Copyright (c) 2021 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module algebra.lie.character
-! leanprover-community/mathlib commit 132328c4dd48da87adca5d408ca54f315282b719
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Lie.Abelian
 import Mathlib.Algebra.Lie.Solvable
 import Mathlib.LinearAlgebra.Dual
 
+#align_import algebra.lie.character from "leanprover-community/mathlib"@"132328c4dd48da87adca5d408ca54f315282b719"
+
 /-!
 # Characters of Lie algebras
 
feat: port Algebra.Lie.Character (#4683)

Dependencies 10 + 523

524 files ported (98.1%)
220014 lines ported (98.5%)
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The unported dependencies are